The modern Greek alphabet has 24 letters. It is used to write the Greek language. The Greek alphabet is also frequently used in science and mathematics to represent various values or variables. Most letters in the Greek alphabet have an equivalent in the English language.

The twenty-four letters (each in uppercase and lowercase forms) are: 

Α α, Β β, Γ γ, Δ δ, Ε ε, Ζ ζ, Η η, Θ θ, Ι ι, Κ κ, Λ λ, Μ μ, Ν ν, Ξ ξ, Ο ο, Π π, Ρ ρ, Σ σ or ς, Τ τ, Υ υ, Φ φ, Χ χ, Ψ ψ, and Ω ω.

The Greek alphabet is thought to be where most European alphabets came from. The alphabet was borrowed from the Phoenician alphabet around the 10th century BC, with many changes to make it fit the Greek language. 

Some of the Phoenician letters for sounds not used in Greek were turned into vowels. The Phoenicians had written their abjad without any vowels, and this is the case with Hebrew and Arabic to the present day. Obviously, their peoples knew how to say the words, so that worked well for them. But the Greek addition of vowels was better for countries where it might be a second language. 

The Greek change made reading easier for trading with other cultures. In general,  Indo-European languages did not use consonant-based roots (where the word's central meaning is based on the consonants) like those in Semitic languages such as Phoenician, Arabic, Hebrew, and Aramaic. 

At first, Greek was written from right to left, same as Phoenician, but after the 6th century BC, it was written from left to right. 

There were some differences in the early Greek alphabet depending on what part of the Greek world it was used in. But over time, all Greeks started to use the same alphabet, especially after the Ionic alphabet of Miletus was officially adopted in Athens in 403 BC. A little later, the rest of Greece did the same, and by 350 BC, during the life of Alexander the Great, almost all Greeks were using the same twenty-four letter Greek alphabet. 

Later, Aristophanes of Byzantium (c. 257185 BC), a Greek scholar and grammarian, invented the three diacritics (accent marks): acute, grave, and circumflex, to mark the tone or pitch of Greek words.

Although the Greek letters accurately represented all the main sounds of the Greek language early on, the sounds of the Greek language changed over time. Some of the vowel sounds began to sound similar to one another, aspirated voiceless stops became voiceless fricatives, and voiced stops became voiced fricatives. One can get an idea of how older Greek pronunciations sounded, by looking at the Latin and English spellings of Greek loanwords like "philosopher", "Chimera", "Cyprus", and "Thessalonica".

Rough breathing or "H" sound 
Another diacritic is a comma, usually above initial vowels. This signaled whether or not the sound of the letter 'H' was present. It is not available in the English standard character-set.  If this comma-like diacritic above the vowel is reversed, it indicates the presence of an /h/ sound before a vowel, diphthong, or rho. Thus, the Greek name Ἕκτωρ is pronounced Hektōr, not Ektor. Another example is ἥρως, pronounced hḗrōs ("hero").

Modern orthography 
In 1982, a new, simplified orthography, known as "monotonic", was adopted for official use in Modern Greek by the Greek state. It uses only a single accent mark, the acute accent. This marks the stressed syllable of polysyllabic words, that is, words with more than one syllable.

Related pages
 Ancient Greek language
 Greek language
 History of the alphabet

References

Other websites 
 Greek alphabet
 Greek Unicode Issues