Ancient Greek grammar is morphologically complex and preserves several features of Proto-Indo-European morphology. Nouns, adjectives, pronouns, articles, numerals and especially verbs are all highly inflected. This article is an introduction to this morphological complexity.

Nouns
The alpha declension contains predominantly feminine nouns. Such nouns have stems ending in short or long alpha. In certain circumstances the alpha changes its length or becomes eta.
In the table below of feminine nouns there are three examples: long alpha stem (ᾱ-stems), short alpha stems (α-stems), and stems which can end in eta (η-stems).
The short alpha stem is not present in masculine nouns, thus only ᾱ-stems and η-stems are declined.

Omicron Declension (second declension)
The labial and velar declension nouns have stems that end in either a labial plosive (β, π, φ) or a velar plosive (γ, κ, χ). When followed by σ/ς, none of these consonants maintain their distinction of voice or aspiration, and join with σ/ς to become ψ or ξ respectively. All nouns are declined the same regardless of gender.

Labial and Velar Declension (third declension)
Attic Greek has a definite article, but no indefinite article. The definite article agrees with its associated noun in number, gender and case. Proper names usually take the definite article. Adjectives are either placed between the article and noun or after the noun, in which case the article is repeated before the adjective. Dependent genitive noun phrases are positioned in exactly the same way, even though this frequently results in splitting the article and noun by a long dependent phrase. For example, τὸ τοῦ ἀνθρώπου ἔργον 'tò toû anthrṓpou érgon', literally "the (of the man) deed", or "The deed of the man." In earlier Greek, for instance Homeric Greek, there was no definite article as such, the corresponding forms still having their original use as demonstrative pronouns.
The definite article is declined thus:

The Article
The numerals from 1 to 10 are:
Numbers one through four are declined.

Numerals
The Ancient Greek verbal system preserves nearly all the complexities of Proto-Indo-European.
In Ancient Greek, verbs have four moods (indicative, imperative, subjunctive and optative), three voices (active, middle and passive), as well as three persons (first, second and third). Verbs are conjugated in four main tenses (present, aorist, perfect, and future), with a full complement of moods for each main tense, although there is no future subjunctive or imperative. In addition, for each main tense there exist, in each voice, an infinitive and participles. Indicative forms of the imperfect, pluperfect and the rare future perfect also exist. The distinction of the "tenses" in moods other than the indicative is predominantly one of aspect rather than time.
A distinction is traditionally made between the so called athematic verbs, with endings affixed directly to the root (also called mi-verbs) and the thematic class of verbs which present a "thematic" vowel /o/ or /e/ before the ending. All athematic roots end in a vowel except for /es-/ "be". The endings are classified into primary (those used in the present, future, perfect and rare future perfect of the indicative, as well as in the subjunctive and secondary (used in the aorist, imperfect, and pluperfect of the indicative, as well as in the optative). Ancient Greek also preserves the PIE middle voice and adds a passive voice, with separate forms only in the future and aorist (elsewhere, the middle forms are used).

Verbs
Verbs have six principal parts: present (I), future (II), aorist (III), perfect (IV), perfect middle (V) and aorist passive (VI), each listed in its first-person singular form:
One principal part can sometimes be predicted from another, but not with any certainty. For some classes of verbs, however, all principal parts can be predicted given the first one. This mostly includes contracted verbs (present stem ending in /a/, /e/, /o/) and verbs ending in /eu/ and /izd/. There are also certain other regularities; for example, the stem in part IV often occurs in parts V and VI as well.

Part I forms the entire present system, as well as the imperfect.
Part II forms the future active and middle tenses.
Part III forms the aorist active and middle tenses.
Part IV forms the perfect and pluperfect active tenses, and the (exceedingly rare) future perfect active.
Part V forms the perfect and pluperfect middle tenses, and the (rare) future perfect middle.
Part VI forms the aorist and future passive tenses. Principal parts
The thematic present stem is formed in various ways:

With no suffix. (That is, the thematic endings, beginning with a thematic /o/ or /e/ vowel, is added directly to the verb stem.)
With a suffix /j/, which transforms the final consonant in various complex ways (/pj/, /phj/, /bj/ -> /pt/; /tj/, /thj/, /kj/, /khj/ -> /tt/ (Attic), /ss/ (Ionic); /gj/, /dj/ -> /zd/; /lj/ -> /ll/; /mj/ -> /jm/; /nj/ -> /jn/; /rj/ -> /jr/). Because stems in /g/, /k/ and /kh/ tend to become indistinguishable in other tenses (likewise for /d/, /t/, and /th/), the /tt/ and /zd/ presents were easily interchanged, with the tendency for all dental stems to move into the /zd/ class and all velar stems into the /tt/ class.
With a suffix /sk/.
With a suffix and/or infix /n/. Present tense
An additional, extremely important class is that of contracted verbs, where the stem itself ends in a vowel, and the vowel contracts with the initial (thematic) vowel of the endings. There are three varieties, depending on whether the stem ends with /a/, /e/ or /o/, and the details of contraction are extremely complex. The earliest contract verbs arose from loss of intervocalic /s/ or /j/, when the latter (the present stem suffix /j/) was added to noun stems ending in a vowel; but soon, these verbs were formed directly from noun stems (so-called denominative verbs). Many later verbs were derived by analogy from various other kinds of nouns (compare the development of the denominative -āre, -ēre, and -īre classes in Latin, with -āre eventually becoming dominant regardless of the noun declension on which the verb was based).

Contracted verbs
The future stem is normally formed from the verb stem (minus any present suffix) with /s/ added and a preceding short vowel lengthened. Verb stems in /m/, /n/, /l/ and /r/, however, as well as most stems in izd, usually add /e/ instead (deleting the zd in the case of these verbs), and form contracted futures, conjugated like contracted presents. (Note: Verb stems in /a/, /e/ and /o/, which form contracted presents, do not have contracted futures; rather, they have futures ending in /ēs/, /ēs/, and /ōs/, respectively. One verb, however, kaleō (kalô) "I call", forms a future based on its root /kal/. This will be a contracted future; hence, the present and future of this verb are both contracted and both nearly identical.)

Future tense
The aorist stem is formed in three basic ways, with three corresponding sets of endings:
The aorist indicative (but no other form) also has an augment added onto the beginning.
Occasionally, two different aorists exist for a single verb, with different meanings: A first (or second) aorist with a transitive meaning, and a root aorist with an intransitive meaning. This was the origin of the aorist passive, which takes active athematic endings.
The aorist passive comes in two varieties, first and second. The first aorist adds thē onto the verb stem, while the second adds ē. Active athematic endings are added onto this.

First or weak aorists add /s/ onto the verb stem (with a preceding short vowel lengthened, as for the future). The first aorist endings mostly begin with a thematic /a/, so alternatively the stem can be said to end with /sa/. (Note that the /s/ is absorbed following an /m/, /n/, /l/ or /r/, with compensatory lengthening of the preceding vowel. This is called a krypto-sigmatic aorist, as the s is "hidden".) Following a /p/ or /k/ (pi or kappa) the sigma combines with the preceding character to form /ps/ and /x/ (psi and xi) respectively. Following a /z/ (zeta/zdeta) the sigma replaces the /z/ character entirely as /zs/ or /zds/ (according to many schools of pronunciation) is too difficult to pronounce.
Second or strong aorists are formed by removing any present suffix or infix, and reducing the root vowel (to the zero-grade of Indo-European ablaut) if possible (mostly ei -> i). Some second aorists are formed by suppletion, i.e., the use of a completely different stem from the present form. Second aorists add the same endings as for the imperfect (in the indicative) and the present (all other moods, plus infinitives and participles); hence, the second aorist stem can never be the same as the present stem.
Root or athematic aorists. The stem assumes a form ending in a long vowel, and athematic endings are added directly onto it. Aorist tense
The perfect tense involves reduplication of the beginning of the stem (see below).
The perfect active stem (principal part IV) comes in two varieties:
The endings are the same in both cases.
The perfect middle stem (principal part V) is formed by direct addition of middle endings onto the (reduplicated) verb stem, with a preceding short vowel sometimes lengthened.
Occasionally, two different perfect actives exist for a single verb, with different meanings, analogously to aorists: A first perfect with a transitive meaning, and a second perfect aorist with an intransitive meaning. From prāttō "I do, I fare": peprākha "I have done", peprāga "I have fared". From phainō "I show": pephanka "I have shown", pephēna "I have appeared".
Sometimes the intransitive form of a perfect has a present meaning.
From (ap-)ollūmi "I destroy, I lose": (ap-)olōleka "I have destroyed, I have lost", (ap-)olōla "I am ruined". From peithō "I persuade": pepeika "I have persuaded", pepoitha "I trust".
Sometimes only one perfect exists, with a present, intransitive meaning. From histēmi "I set, I cause to stand": hestēka "I am standing". From rhēgnūmi "I break": errhōga "I am broken". From (apo-)thnēiskō "I die": tethnēka "I am dead". From mimnēiskō "I remind": memnēmai (middle) "I remember". From egeirō "I arouse": egrēgora "I am awake". From ktaomai (middle) "I acquire": kektēmai (middle) "I possess".

First perfect, which usually adds k (sometimes ēk or ek). A preceding dental is lost and a preceding short vowel sometimes lengthened. The k-perfect is not added directly onto labial-final or velar-final stems; instead, the aspirated perfect is used, with a final labial becoming ph and a final velar kh.
Second perfect, which adds no suffix, but may modify the root vowel (into the o-grade of Indo-European ablaut). Perfect tense
Some verbs, called deponent verbs, have a middle form but active meaning. Most such verbs have no active forms at all. There are two types:
Some verbs have active forms in some stems, middle or passive in others, with no middle or passive meaning. These are called semi-deponents and have many variations:

Middle deponents have middle forms in all stems. These will have principal parts I, II, III and V only (sometimes also part VI, with passive meaning).
Passive deponents (less common) have middle forms in most stems, but passive form in the aorist. These will have principal parts I, II, V and VI only. (Most such verbs still have a middle future, not a passive future.)
Most common are active verbs with middle future stems.
Some verbs are active verbs but with a middle perfect stem (dokeō "seem, think"; eirgō "imprison, prevent"; elenkhō "examine, confute"; thaptō "bury"; skedannūmi "scatter"; sphallō "trip up"; titrōskō "wound").
Some verbs are active verbs but with middle future and perfect stems (e.g., daknō "bite").
Some verbs are middle verbs but with an active perfect stem (e.g., gignomai "become").
Some verbs are middle verbs but with active aorist and perfect stems (e.g., haliskomai "be captured").
Other combinations exist as well. Deponents, semi-deponents

Sample paradigms

A completely regular eu verb: paideuō, paideusō, epaideusa, pepaideuka, pepaideumai, epaideuthēn "educate".
The standard paradigmatic verb: lūō, lūsō, elūsa, leluka, lelumai, eluthēn "free, release; (middle) ransom". (Note variable vowel length. In Homeric Greek, all parts have a short u.)
A regular contracted verb in e: poieō (poiô), poiēsō, epoiēsa, pepoiēka, pepoiēmai, epoiēthēn "make, do".
A regular contracted verb in a: nikaō (nikô), nikēsō, enikēsa, nenikēka, nenikēmai, enikēthēn "win". (Note how /a/ is lengthened to /ē/.)
A regular contracted verb in o: deloō (delô), delōsō, edelōsa, dedelōka, dedelōmai, edelōthēn "show".
A regular verb in izd: nomizdō, nomieō (nomiô), enomisa, nenomika, nenomismai, enomisthēn "consider, think, believe". (Note the normal contracted future in these types of verbs.)
A regular verb in azd: thaumazdō, thaumasō, ethaumasa, tethaumaka, tethaumasmai, ethaumasthēn "marvel at". Verbs in vowel stems

Velar-stem: lēgō, lēksō, elēksa, lelēkha, lelēgmai, elēkhthēn "cease (+ gen.)". (Note regular use of the aspirated perfect.)
Velar-stem: arkhō, arksō, ērksa, ērkha, ērgmai, ērkhthēn "rule". (Note regular use of augment for reduplication in perfect due to initial vowel.)
Labial-stem: graphō, grapsō, egrapsa, gegrapha, gegrammai, egraphēn "write". (Second aorist passive.)
Labial-stem, with present /j/ suffix: blaptō, blapsō, eblapsa, beblapha, beblammai, eblaphthēn/eblabēn "harm". (Both first and second aorist passive with same meaning.)
Dental-stem: peithō, peisō, epeisa, pepeika, pepeismai, epeisthēn "persuade; (middle) obey (+dat.)". (This verb also has a poetic second perfect pepoitha meaning "trust")
Dental-stem: ereidō, ereisō, ēreisa, --, erēreismai, ēreisthēn "(cause to) lean, prop; press hard". (Semi-deponent, with middle perfect; Attic reduplication.)
Sonorant-stem, with present /j/ suffix: aggellō, aggeleō (aggelô), ēggeila, ēggelka, ēggelmai, ēggelthēn "announce". (Regular contracted future, as in all sonorant-stem verbs. Compensatory lengthening in the aorist, caused by the lost /s/, with a -> ē, e -> ei, i -> ī, o -> ou, u -> ū.)
Verb in ainō: sēmainō, sēmaneō (sēmanô), esēmēna, --, sesēmasmai, esēmanthēn "show, point out; signify, indicate". (Semi-deponent, with middle perfect.)
Verb in ainō: kraino, kraneō (kranô), ekrāna, --, kekrammai, ekranthēn "accomplish". (Semi-deponent, with middle perfect, but with slightly different middle perfect from previous verb. Note that ā never changes to ē after r.)
Verb in ūnō: aiskhūnō, aiskhuneō (aiskhunô), ēiskhūna, --, --, ēiskhunthēn "dishonor". (No perfect.)
Present /an/ suffix: aisthanomai, aisthēsomai, ēisthomēn, --, ēisthēmai, -- "perceive". (Deponent. Second aorist. Root aisth with suffix ē in some forms.)
Present /isk/ suffix: haliskomai, halōsomai, heālōn, heālōka, --, -- "be captured". (Semi-deponent, middle with active aorist and perfect. Root aorist. Irregular augment, both syllabic and quantitative – transfer of /h/ to beginning is normal. Suffix ō in some forms.)
Reduplicated present, with /sk/ suffix: gignōskō, gnōsomai, egnōn, egnōka, egnōsmai, egnōsthēn "know". (Semi-deponent with middle future. Root aorist. Irregular reduplication with augment. Suffix /s/ in parts V and VI.) Verbs in consonant stems, no ablaut

Labial-stem: leipō, leipsō, elipon, leloipa, leleimmai, eleiphthēn "leave". (Second aorist. Ablaut leip/lip/loip.)
Labial-stem: trephō, threpsō, ethrepsa, tetropha, tethrammai, etraphēn, etrephthēn "rear, bring up, nourish". (Second aorist passive. t/th alternation due to dissimilation of aspirates (Grassmann's law). Ablaut t(h)reph/t(h)roph/t(h)raph.)
Velar-stem: echō, heksō/skhēsō, eskhon, eskhēka, -eskhēmai, -- "have, hold". (Second aorist. Perfect middle occurs only in compounds. h/nothing alternation at beginning of stem due to dissimilation of aspirates (Grassmann's law). Ablaut (h)ekh/skh. Suffix ē in some forms.)
Sonorant-stem, with present /j/ suffix :speirō, spereō (sperô), espeira, esparka, esparmai, esparēn "sow". (Second aorist passive. Ablaut sper/spar.)
Sonorant-stem, with present /j/ suffix: ballō, baleō (balô), ebalon, beblēka, beblēmai, eblēthēn "throw, hit". (Second aorist. Ablaut bal/blē.)
Present /n/ suffix: daknō, dēksomai, edakon, --, dedēgmai, edēkhthēn "bite". (Semi-deponent with middle future and perfect. Second aorist. Ablaut dak/dēk.)
Present /nj/ suffix: bainō, bēsomai, ebēn, bebēka, --, -- "go". (Root aorist. Ablaut ba/bē.)
Prefixed verb, present /nj/ suffix: apobainō, apobēsomai, apebēn, apobebēka, --, -- "go away, result". (Prefix precedes augment and reduplication. Final vowel of prefix elided before initial vowel.)
Present /an/ suffix, nasal infix: lambanō, lēpsomai, elabon, eilēpha, eilēmmai, elēphthēn "take". (Semi-deponent with middle future. Second aorist. Ablaut lab/lēb. Irregular reduplication.)
Present /an/ suffix, nasal infix: punthanomai, peusomai, eputhomēn, --, pepusmai, -- "ascertain". (Deponent. Second aorist. Ablaut puth/peuth.)
Reduplicated present: gignomai, genēsomai, egenomēn, gegona, gegenēmai, -- "become". (Semi-deponent, middle with active perfect. Second aorist and perfect. Ablaut gen/gon/gn. Suffix ē in some forms.)
Reduplicated present: pīptō, pesoumai, epeson, peptōka, --, -- "fall". (Semi-deponent with middle future. Second aorist. Ablaut pet/pt/ptō. Irregular long vowel in present reduplication. Irregular occurrence of contracted future. Irregular suffix s in future and aorist.)
Present /sk/ suffix: paskhō, peisomai, epathon, pepontha, --, -- "suffer". (Semi-deponent with middle future. Second aorist and perfect. Ablaut penth/ponth/path. Irregular assimilation of aspiration into present /sk/ suffix.)
Present /isk/ suffix: apothnēiskō, apothanoumai, apethanon, tethnēka, --, -- "die". (Semi-deponent with middle future. Second aorist. Ablaut than/thnē. No prefix in perfect; perfect means "be dead". Irregular occurrence of contracted future.) Verbs with ablaut
These verbs have reduplication in the present, ablaut between short and long forms, a separate set of endings, and certain other irregularities that vary from verb to verb.

didōmi, dōsō, edōka, dedōka, dedomai, edothēn "give".
hīēmi, hēsō, hēka, heika, heimai, heithēn "let go, send forth".
histēmi, stēsō, estēsa (trans.) or estēn (intr.), hestēka (intr.), hestamai, estathēn "make stand; (middle or intr.) stand".
Prefixed verb: aphistēmi, apostēsō, apestēsa (trans.) or apestēn (intr.), aphestēka (intr.), aphestamai, apestathēn "cause to revolt; (middle or intr.) revolt". Athematic verbs
These verbs all have complex irregularities, ablaut, second aorist and/or perfect, unexpected reduplication and/or augment, etc.

erkhomai, eîmi, ēlthon, elēlutha, --, -- "go, come".
legō, eraō (erô)/leksō, eipon/eleksa, eirēka, eirēmai/lelegmai, elekhthēn/errhēthēn "say, speak".
horaō, opsomai, eidon, heorāka/heōrāka, heōrāmai/ōmmai, ōphthēn,oida "see".
pherō, oisō, ēnegka, ēnegkon, enēnokha, enēnegmai, ēnekhthēn "carry".
esthiō, edomai, ephagon, edēdoka, edēdesmai, ēdesthēn "eat".
pōleō, apodōsomai, apedomēn, peprāka, peprāmai, eprāthēn "sell". Suppletive verbs

Time and aspect
The rules on mood sequence (Consecutio modorum) determine the mood of verbs in subordinate clauses in a way analogous to but more flexible than the Latin rules on time sequence Consecutio temporum which determine their tense.
Putting aside special cases and exceptions, these rules can be formulated as follows:

In dependent sentences, where the construction allows both the subjunctive and the optative, the subjunctive is used if the leading verb is primary, and the optative if it is secondary. E.g. Πράττουσιν ἃ ἂν βούλωνται, they do whatever they want; but Ἔπραττον ἃ βούλοιντο, they did whatever they wanted.
Similarly, where the construction allows both the indicative and the optative, the indicative follows primary, and the optative follows secondary tenses. E.g. Λέγουσιν ὅτι τοῦτο βούλονται, they say they want this; εἶπον ὅτι τοῦτο βούλοιντο, they said they wanted this.