Ancient Greek verbs, just like ancient Greek nouns, have multiple different forms.  This will all be familiar to you if you’ve studied just about any European language (even English has vestiges of this system, although they’re much reduced for most verbs).  There are six forms, first person singular (I do), second person singular (you do), third person singular (he/she/it does), first person plural (we do), second person plural (y’all do – Greek, like just about every language on the planet except for English, makes a distinction between one ‘you’ and many ‘you’s), and third person plural (they do).  For most English verbs, of course, only one of these forms varies at all – the third person singular, which typically has an -s on the end.  In Greek though (as well as Latin, French, German, Spanish, Italian, Portuguese, etc) the six forms are markedly different.  Here are the forms of the Greek verb λυω – to loosen, release, or free:

λυω – first person singular; I free
λυεις – second person singular; you free
λυει – third person singular; he/she/it frees
λυομεν – first person plural; we free
λυετε – second person plural; y’all free
λυουσι(ν) – third person plural; they free

N.B. The (ν) on the end of the third person plural form means that this form will end with a ν if the next word begins with a vowel, but will leave the ν off if the next word ends in a consonant – exactly like a(n) in English.

These endings can be transferred to any regular verb – so the word for ‘stop,’ παυω (where the English word ‘pause’ comes from) will be παυει if you’re saying “he stops” or “the farmer stops” or whatever, and παυουσι if you’re saying something like "they stop" or “the farmers stop."  Because Greek has all of these forms, which are for the most part very easily distinguished, there are a lot of words which will often be left out of a Greek sentence.  For example, Greek does have a word for "I” – ἐγω, whence the English ‘ego’ – but very rarely uses it, since a reader or listener can always tell from the -ω ending of the verb that the subject of a sentence is “I.”

It becomes rather more complicated if the ‘stem’ of the verb (the unchanging part) ends in a vowel.  The vowels ε, α, and ο at the end of a verb’s stem will merge into the vowels of the suffix, changing the spelling and pronunciation.

ε is the weakest of those sounds, and is normally ‘swallowed up’ entirely by the sound of the verb ending, but does alter the first person plural and second person plural.  The verb φιλεω, to love, for instance, goes like this:

φιλω – I love
φιλεις – you love
φιλει – he/she/it loves
φιλουμεν – we love – note the ου sound, where λυω just had an ο sound
φιλειτε – y’all love – again, note the ει where λυω had an ε
φιλουσι(ν) – they love

Verbs with stems ending in α, such as ὁραω, to see, go like this:

ὁρω – I see
ὁρᾳς – you see – note the iota subscript beneath the alpha, which is a ‘remnant,’ if you like, of the iota in the standard ending
ὁρᾳ – he/she/it sees – again with an iota subscript
ὁρωμεν – we see
ὁρατε – y’all see
ὁρωσι(ν) – they see

Finally, verbs with stems ending in ο, such as δηλοω, to show or reveal (there are very few of these), go like this:

δηλω – I show
δηλοις – you show
δηλοι – he/she/it shows
δηλουμεν – we show
δηλουτε – y’all show
δηλουσι(ν) – they show

Note that verbs like this will be listed in a dictionary as φιλεω, ὁραω, δηλοω, etc, with the end vowel present, even though none of these forms actually exist in practice because all three vowels get swallowed up completely by the omega of the first person singular ending (well… unless you’re speaking Ionic, but let’s not go there).

All of this covers present active indicative verbs.  Present is a tense, of course, active is what we call a ‘voice,’ and indicative is what we call a ‘mood.’

You’re probably used to thinking that there are three tenses, right?  Past, present, and future?  Well, not exactly.  Greek has six tenses – and before you protest that that’s way too complicated, English actually has twelve; it’s just that we normally don’t consciously think of them in that way.  The English tenses are present, present perfect, past, past perfect, future, and future perfect, each of which comes in ‘simple’ and ‘continuous’ flavours – ‘I see’ and ‘I am seeing,’ for instance, are actually different tenses; one is present simple and the other is present continuous.  “I will see” and “I will have seen,” likewise, are two different things – one is future simple, and the other is future perfect simple.  The Greek tenses are present, future, imperfect (roughly equivalent to our past continuous tense – “I was seeing”), perfect (this is closest in meaning to our present perfect – “I have seen”), pluperfect (our past perfect, “I had seen”), and aorist.  The aorist is the “timeless” tense (the term comes from a Greek word meaning “without boundaries”).  It’s the closest thing Greek has to a simple past, which is what it most often means, but in many contexts it can in fact be used to express present or even future action.  It’s also the tense used for statements of universal truth (which in English we would normally put into the simple present).  The aorist tense is, hands down, the hardest thing about learning Greek; it is an utter bastard, and it is probably the most common tense in the language (more common, I suspect, than the present) so there’s no way you can avoid the damn thing.

Greek is packed full of verbs that have irregular ways of getting into the different tenses, but the more sensible ones look like this:

Future: add a sigma to the end of the stem, then use present tense endings: λυσω, λυσεις, λυσει, etc.

Imperfect: add an epsilon to the beginning of the stem, then use a new set of endings: ἐλυον, ἐλυες, ἐλυε(ν), ἐλυομεν, ἐλυετε, ἐλυον (notice similarities with corresponding present endings, and also that first person singular and third person plural are identical).

Perfect: repeat the first consonant, with an epsilon after it, and use another set of endings: λελυκα, λελυκας, λελυκε(ν), λελυκαμεν, λελυκατε, λελυκαν.

Pluperfect: add an epsilon to the beginning of the perfect stem, then use yet another set of endings (mostly similar to the perfect endings, with epsilons instead of alphas): ἐλελυκε, ἐλελυκες, ἐλελυκε(ν), ἐλελυκεμεν, ἐλελυκετε, ἐλελυκεσαν.

Aorist: add an epsilon to the beginning of the stem and a sigma to the end of the stem, then use more new endings: ἐλυσα, ἐλυσας, ἐλυσε(ν), ἐλυσαμεν, ἐλυσατε, ἐλυσαν.  Or, alternatively… well, there are four kinds of aorist in Greek.  I call them nice aorists (follow the nice rule that λυω follows), weird aorists (change the stem a little bit, in a more or less random fashion, then use the imperfect endings – μανθανω becomes ἐμαθον, πασχω becomes ἐπαθον, etc), dumb aorists (change the stem to something completely unrelated, just to fuck with you – τρεχω becomes ἐδραμον, ὁραω becomes εἰδον, etc), and retarded aorists (just give up and reduce the stem to one letter, then use whatever the hell endings you feel like – βαινω becomes ἐβην, γιγνωσκω becomes ἐγνων, etc).

You can see why the aorist tense is the trickiest part of this language.

Anyway.  Voices.

You’ve all met voices before – English has two of them, active and passive.  This is the distinction between “I see” and “I am seen."  Easy, right?  How complicated can this possibly get?  Active.  Passive.  Done.

Well, the thing is, Greek has both of those things, but it also has something better: the ‘middle’ voice.  This does not exist in English (in fact, I don’t know of any other languages that have a middle voice – Latin seems to have had it at one point, but has lost it almost completely by the classical period), and as a result it is rather difficult to explain succinctly.  It’s best to think of it has having three different flavours of meaning.  Where the active is "I see” and the passive is “I am seen,” the middle is something like “I see myself” or “I see for my own benefit” or “I cause to be seen."  Middle verbs are a remnant of an ancestral Proto-Indo-European system whereby verbs, instead of being either active or passive, were instead ‘inward’ or ‘outward,’ if you will – one for actions which primarily affected oneself, the other for actions which primarily affected other things or people.  For some verbs, you can easily see how this makes sense – for instance, the verb ἐγειρω means ‘to wake up,’ and its active form refers to waking someone else, while its middle form refers to just waking up in the morning.  Others… not so much.  Greek has two common verbs for wanting or being willing – ἐθελω and βουλομαι.  The former is normally active, the latter is always middle.  No clue why.

Middles, of course, have their own sets of endings in all the different tenses.  Here are just the present indicative ones:

λυομαι
λυει (note that this looks just like the third person singular of the active form of the verb), alternatively sometimes λυῃ (note the iota subscript)
λυεται
λυομεθα
λυεσθε
λυονται

Finally, there’s moods.  Whenever you make a simple statement, you are using an ‘indicative’ verb – a verb that ‘indicates’ the truth of something, if you like.  There are four others you need to know.  One is the imperative, the mood of command – whenever you tell someone to do something, you are using an imperative.  The imperative forms of λυω are λυε (singular) and λυετε (plural – the plural imperative ending is always the same as the second person plural indicative ending, for every verb in Greek).  The next mood is the infinitive.  This is the form we mark with "to” in English – “to run,” “to see,” “to speak,” etc.  It’s used a lot less in Greek than in English, because we tend to use infinitives to indicate purpose (“I went to London to see the Queen”), which Greek doesn’t, but it gets used for things like “I want to see” and “I seem to see.”  The infinitive form of λυω is λυειν.  Next is the subjunctive, the mood of possibility.  Subjunctives indicate stuff that ‘might,’ ‘could’ or ‘would’ happen, among other things.  Subjunctive endings normally lengthen their vowel sound, like so: λυω, λυῃς, λυῃ, λυωμεν, λυητε, λυωσι.  Finally, you have optatives, which theoretically express wishes and desires, although in Greek the boundaries between situations that use subjunctives and situations that use optatives can become a little blurry at times.  Present active optatives are characterised by an ‘oi’ sound in their endings: λυοιμι, λυοις, λυοι, λυοιμεν, λυοιτε, λυοιεν.

Now, here’s where it gets worse.

Every verb has a mood, a voice, and a tense – so all of those have to be multiplied together.  Six basic forms, times three moods (indicative, subjunctive and optative), plus one infinitive and two imperatives, times three voices, times six tenses makes 378 different forms for each Greek verb (of course, some verbs don’t have active forms, and the perfect and pluperfect tenses are both very rare, but still) and that’s not even counting the schizophrenic ones like λεγω that have more than one aorist stem (in this case, a nice aorist – ἐλεξα – and a far more common dumb aorist – εἰπον).  If it’s a nice verb like λυω or παυω, you can work out all of those forms from scratch using simple rules.  If it’s a verb like ὁραω that does something crazy and unexpected in just about every tense (future ὀψομαι, aorist εἰδον, perfect οἰδα, pluperfect… hell, who am I kidding? I have no idea what the pluperfect of ὁραω is) then you’re in trouble.  And then, of course, you have the verbs that just plain hate you, like εἰμι, the verb ‘to be,’ which is spectacularly irregular in just about every language in history (look at English: I am, you are, he/she/it is, I was, you were, I have been, to be – what the hell?).  And don’t even get me started on the aorist passive.

Then, of course, once you successfully learn all of that, you discover that some authors (Homer, I’m looking at you) will blithely ignore rules, use all manner of obscure variant forms, add or drop syllables on a whim, and just generally make things up in order to have the words fit their poetic meter more effectively.  And then you’re trekking through Aristophanes when you discover that the great man has decided to string four or five words together, in the style of modern German, to create a great superword like ἀρχαιομελισιδωνοφρυνιχηρατα, which takes up a whole line of iambic trimeter on its own and reduces the less able among us to fits of terror…

It’s enough to make one give up and stick to Latin.