Greek language has three different vowels and three diphthongs (= pairs of vowels) that possess the soundi, like in the English word ill: ι, η, υ, ει, οι, υι.

Letters Pronunciation
Ι,ι i l like in the word eel
Η,η i l like in the word eel
Υ,υ i l like in the word eel

Diphthongs Pronunciation
ΕΙ,ει i like in the word eel
ΟΙ,οι i like in the word eel
ΥΙ,υι i like in the word eel

In modern GreekΙ,ι, Η,η, Υ,υ, ΟΙ, οι, ΕΙ,ει, ΥΙ, υιpossess the same sound and value. There is no difference in their pronunciation. Only when the syllable gets the tonos (=accent) on it, it is accented (louder and a bit longer): ΗΜυτιλήνη (EE mitiLEEni = Mytilene), οιΔελφοί (EE deLFEE = Delphi).
Things were different for the ancient Greeks who have inherited this writing to us. Obviously, those who invented the words and their spelling had decided to use different vowels for the sound i. Have they applied any grammatical rules for their use? Was there any difference in their pronunciation?
Though not in all cases, they had rules for their spelling and grammatical use as well. Η, η, ΟΙ, οι and ΕΙ, ει werelongvowels. That means that the duration of their sound was the double of the short letters. Ι,ιΥ,υ were sometimes short and sometimes long letters, depending on the consonants that followed. The diphthongs ΟΙ, οι, ΕΙ, ει, had usually a long value and sound. When the diphthong ΟΙ, οιwas found at the end of a noun or adjective (for instance in their plural), its value and sound was short.
In modern Greek language we don’t have long and short vowels regarding the duration of their sound. Nevertheless, we have kept some rules regarding the spelling of the words. Here are some rules, which we still apply today in modern Greek.
RULE ONE
Neuter grammatical gender words, nouns and adjectives, end in the singular number either in -οor in -ι. Then they are always written with Ι,ι: Τοπαιδ-ί (TO peDEE = the child), τοσπίτ-ι (TO SPEEti = the house), τομολύβ-ι (TO moLEEvi = the pencil).
RULE TWO
The feminine grammatical gender article in the singular number is Η,η.Unlike English, we usually put the article before the name:ΗΕλένη (EE eLEni = Helen), ηΝίκη (EE NEEki = Nike), ηΚαίτη (EE KEti = Kate).
RULE THREE
The feminine grammatical gender article in the plural number is ΟΙ, οι. Οιμαμάδες (EE maMAdes = the moms), οιγιαγιάδες (EE yiayiAdes = the grandmothers).
RULE FOUR
Feminine grammaticαl gender nouns and adjectives in the singular number, nominative case, end either in -α or in -η. This is the reason why all Greek feminine names ending in the sound i are always written withΗ,η: ΗΕλέν-η, ηΚαίτ-η.
RULE FIVE
Masculine grammatical gender nouns and adjectives in the plural number, nominative and votive cases, end in OI, οι: οικαλοίάνθρωποι (EE kaLEEAnthropi = the good people), οικακοίσκύλοι (EE kaKEESKEEli = the bad dogs).
RULE SIX
The third person singular of the active voice verbs always ends in ει: κάν-ει (KAni = he/ she /it does), τρώ-ει (TROi = he/ she/ it eats), πίν-ει (PEENi = he/ she/ it/ drinks).

PRONUNCIATION KEY
i (ill), ee (beer), e (ever), o (organ), oo (boot), y (yes), h (helium), th (theory), d (the). The capitalized syllables are accented.