Greek is one of the oldest attested Indo-European languages, known from 1400 BC in inscriptions in a syllabary of Minoan origin. The present alphabet was introduced by a Phoenician called Qadmu (Καδμος) about 800 BC, and has been in use, with a few letters added and removed, continuously since then. The 24-letter alphabet used in Classical Greek is the same one used today. Greek is the official language of both Greece and Cyprus, but is only spoken in the south of the latter.
Many Greek words have been borrowed into other languages, so you will find a lot of these words familiar, such as τραυμα (trauma, "injury") and σοφία (sofia "wisdom, knowledge"). Originally they were borrowed into Latin, which became the Romance languages. The changes Greek words underwent in Latin are different from those they underwent in Greek. For instance, in a rare case of someone actually returning a word he borrowed, κινημα (kinema, motion) was borrowed into Latin as cinema, which in French acquired the meaning "movie", and was returned to Greek as σινεμα (sinema).
Greek has changed less in the last two thousand years than English has in the last five hundred. It still has three genders, five cases, and movable ν. Although the dative dropped out of use in Greek before the dative merged with the accusative in English, one can still form the dative of μπαγλαμας (a stringed instrument smaller than the μπουζουκι), even though it belongs to a new declension. So if you know some Attic or Koine Greek and pronounce it as Modern Greek, though you will sound archaic, you will probably be understood.
Following are the uppercase and lowercase versions of each letter, followed by its name in English (Latin) and Greek. (You can also see how the transliteration works)
Α/α alpha (άλφα)
as in pat
Ε/ε epsilon (έψιλον)
as in pet
Η/η eeta (ήτα)
as in reed
Ι/ι iota (ιώτα)
as in reed, though when followed by a vowel it can often be pronounced like y - example: its very name, it's either said as iota or yota.
Ο/ο omicron (όμικρον)
as in pot
Υ/υ eepsilon (ύψιλον)
as in reed
Ω/ω omega (ωμέγα)
as in pot
as in pet; If you want to pronounce AI as in British English "icon" use the ϊ; the same rule applies to all other dipthongs with the I letter.
as in wheat
as in wheat
as in wheat
as in pool
For the last two diphthongs: when followed by a voiceless consonant or a vowel or nothing (end of the word), the upsilon is pronounced as f resulting to 'af' and 'ef'; though, when followed by a voiced consonant the f is voiced as well making it a v.. so we have 'av' and 'ev'. (example: 'aura' and 'tau' in Greek are pronounced as 'avra' and 'tav'; although "au" and "eu" are increasingly pronounced among the younger generation, 45 years and under.)
Consonants and such Clusters
Β/β veeta (βήτα)
Γ/γ gamma (γάμμα)
a voiced version of chi, as w in woman, but stronger. Before epsilon (γε) and iota (γι), as in yet and yiddish. Also see consonant clusters.
Δ/δ thelta (δέλτα)
as in those / Spanish soft d as in "nido" / Norse Ð/ð
Ζ/ζ zeeta (ζήτα)
as in zone
Θ/θ theeta (θήτα)
th as in thorn / Norse Þ/þ
Κ/κ kappa (κάππα)
as in kinetic
Λ/λ lamtha (λάμδα)
Μ/μ mee (μι)
Ν/ν nee (νι)
Ξ/ξ ksee (ξι)
X/x as in ax
Π/π pee (πι)
P/p as in ape
Ρ/ρ rho (ρο)
Σ/σ/ς sigma (σίγμα)
S/s as in some. Before voiced consonants it gets voiced to z
Τ/τ taf (ταυ)
Φ/φ fee (φι)
Χ/χ hee (χι)
Scottish ch [loch] / like an H/h but with the tongue touching the palate
Ψ/ψ psi (ψι)
as in lips
SPECIAL CONSONANT CLUSTERS:
as in gong
as in gong
n+hee / like ngh in Buckingham: Μπάκιγχαμ
as in bumble / B/b. At the beginning of the word is read just as b. Inside the word is pronounced like mb
as in dander / D/d. At the beginning of the word is read just as d. Inside the word is pronounced like nd
All the above 5 diphthongs can be nasalized more or less depending to the speaker.
Any other consonant combination is pronounced like their English counterparts.
Just remember which is the proper letter in English!
Notes on Sounds, Accents etc.
The accent (similar in usage as in Spanish), if written, is placed on the vowel of the tonic syllable, or onto the second vowel if there's a diphthong. If there's an accent at the first vowel of a diphthong, or a diaeresis on the second, then it isn't an actual diphthong and the two vowels are pronunced separately. The former occasion is the most common, but since words written in capital letters never get accents, the diaeresis is the only way to note the broken diphthong at all-caps phrases - English such example: naïve. (diairesis = two dots on top of iota or upsilon, Ϊ/ϊ - Ϋ/ϋ)
All vowels have the same short length. So yes, there are 2 ways to write 'e', 6 to write 'i' and 2 letters to write 'o'!
Diphthongs 'γγ' and 'γχ' are never found at the start of a word. Vowel diphthong 'υι' is very rare, virtually only in a couple words.
Greek language lacks a 'sh' sound. Consequently there are only simple unaspirated s, z, ts, j, x 's (no shame, pleasure, luxurious, chin etc.). Also, "ς" is the form of Sigma used only when it is the last letter of a word. Graphically it looks like English s.
The capital letters are more or less the same with the ones of the English alphabet. Although the small letters seem entirely different (and some of them are indeed) at people's handwriting they can be extremely close to English.
Note also that Greek punctuation differs a little: The Greek question mark (ερωτηματικό) is just like the Latin semi-colon ; . While the Greek semi-colon (άνω τελεία) is like the full stop "flying" just above the line •.
Greek people know they have a difficult language (for foreigners) and don't expect any tourist to know more than a couple words. And even while they think it's easy phonetically, they understand the problems foreigners have pronouncing it. You can say gamma as a hard 'g', chi as 'h', and rho as an unrolled English 'r', you can also say "au" or "eu" instead of "av" and "ev" and you'll be totally understood. People in no way expect you to be proficient in any aspect of Greek, so by studying a bit before visiting you can really impress people and win their hearts! Of course, it will require serious effort and dedication to learn to speak Greek fluently, as Greek grammar is admittedly more complex than it is in most other languages (much more demanding than German, for example, which is a language with relatively complex grammar). But still, you can master relatively easily the fundaments of communication and get your meaning across. And even if you don't, don't despair: almost all Greeks (but the oldest) can understand and speak English.