Although the earliest forms of Greek were written using a syllabary, for most of its history, Greek has been written using the Greek alphabet. The alphabet appeared on the scene approximately 2,700 years ago. It is adapted from the Phoenician alphabet, and the most notable change is the use of letters to represent vowel sounds. Although earlier variations of the alphabet included additional letters, most extant ancient Greek writing is written using the 24 letters of the Greek alphabet in its current form.
In Phoenician, each of the letters was named after an object whose name began with that letter. For example, the name of the first letter was “aleph”, which meant ox. The Greeks borrowed the names of the letters along with the symbols and naturalized the pronunciation, so “aleph”, “bet” and “gimel” became “alpha”, “beta” and “gamma” and lost the connection with the original meaning of the names
Just as the Greeks borrowed the alphabet from the Phoenicians (changing it to suit their needs), many other alphabets in use today were developed from the Greek alphabet (including the Latin alphabet used to write English and the Cyrillic alphabet used to write Russian). Greek letters also appear outside of the written Greek language in various forums, including mathematics and fraternity names. As a result, for the average Westerner, the Greek alphabet is not entirely foreign.
Here is a list of the Greek letters:
Α, Β, Γ, Δ, Ε, Ζ, Η, Θ, Ι, Κ, Λ, Μ, Ν, Ξ, Ο, Π, Ρ, Σ, Τ, Υ, Φ, Χ, Ψ, Ω
As mentioned above, many of these symbols will be familiar to a speaker of English. However, not all represent the same sounds in ancient Greek as in English. For example, P is a bilabial plosive in English (eg, the “p” in “pat”), but represents the “r” sound in ancient Greek.
For more information on the ancient Greek alphabet, you can view the wiki page at http://en.wikipedia.org/wiki/Greek_alphabet.