Thematic Vowel

Verb Conjugation

It is usual to say that there are 2 different types of verbs in ancient Greek, with different conjugation patterns:

-ω verbs and
-μι verbs

Thematic versus A-thematic

-ω verbs insert a vowel between the stem and the personal ending. This vowel is called thematic vowel. The word itself is obviously derived from τίθημι (to put, place).
-μι verbs (like τίθημι for instance), in the present tense complex, do not insert such a vowel and are therefore also sometimes called a-thematic (privative α meaning no extra vowel inserted). The personal endings are added straight onto the stem of these verbs. In the present tense complex.

To make the difference "thematic versus athematic" clear, compare the thematic imperfect of λύω (I release, let go) with the a-thematic imperfect of δείκνυμι (I show).
I have chosen the imperfect because this is where the thematic vowel is most clearly discernible. (In the present, contractions between thematic vowel and endings confuse the issue somewhat.)
And it also shows quite clearly that ο is used before μ and ν and
And it also shows quite clearly that ε before all else.
Well, good enough for now, we'll add some more later on.

Compare:

Imperfect
was releasing thematic			Who?	was showing a-thematic
ἔλυ	ο	ν	I	ἐδείκνῡ	ν
ἔλυ	ε	ς	you (sg)	ἐδείκνῡ	ς
ἔλυ	ε		he, she, it	ἐδείκνῡ
ἐλύ	ο	μεν	we	ἐδείκνυ	μεν
ἐλύ	ε	τε	you (pl)	ἐδείκνυ	τε
ἔλυ	ο	ν	they	ἐδείκνυ	σαν

You may have noticed that I did mark the ypsilon υ with a macron in the singular of δείκνῡ-μι, but not in the plural. That is another difference between thematic and athematic verbs:

In the present indicative, imperfect and imperative, active voice only, the stem-vowel is always long in the singular, but short in the plural of -μι verbs. Whereas the stem-vowel of -ω verbs keeps the same length in ALL of its forms (either all long, or all short).