I have learned ancient Greek at school and my question is: "Is the pronounciation of the letters in the modern Greek alphabèt the same as the Ancient's or is there a difference between them?"
Τhere are only speculations how Ancient Greek were really pronounced. Of course nobody had ever heard an Ancient Greek speaking :) But some texts help to restore some sounds. For instance a verb for the sound of the sheep is βληχώμαι, that has passed to the Modern Greek too (katharevousa) and βελάζω (demoteke). But the sheep makes a sound like be be, not βε βε. So more likely the ancient β was like a b. But it depends on the period we are talking about. In the Ancient Greek Koene there had been very important changes, either in Grammar or in pronounciation. Greek became a common language (Lingua Franca) in all Eastern Mediterranean and all East after Alexander the Great. So she was spoken by many as a second language, even as a first one, who had no Greek origin. These people had many difficulties to spell the Ancient Greek and Greek started becoming more simplified, became more analytic in syntax and the Grammar easier. This was the period that the scholars of Alexandria decided to introduce the accents (3 accents) and aspiration (2 aspiration marks) as an aid to pronunciation. Notice that there were nor lower-case letters in that period, these were introduced much later, in the 8th c. AC. From these accents just only one preserved today. But some people insist to use them as an ornament mostly in the phrase, but with no practical use.
My personal view is that Greek have aspiration and stresses that are not written, and not only in words, but in phrases too, as it happens to all languages. Languages is a vivid organisation, so no written form can express everything. But the orthography is historical, so one mastered in Ancient Greek can find similarities with the Modern one, so he can easily learn how to write the Modern Greek word. For sure the written form of Modern Greek is conservative.
To continue the story: Some scholars and authors insisted writing with the Ancient Classic way, but the people continued speaking the language as it was in their everyday life. So a huge gap started creating between them. This problem was maintained almost to our days. The Modern Greek is a mixture of the vulgar, colloquial Greek and the scholastic one, as not all the meanings and terms cannot expressed in the colloquial language. So many Ancient Greek words passed as they were to Modern Greek. In the meantime there are synonyms in informal Greek of foreign origin, as Slavic, Italian and Turkish (some of them came from Arabic and Farsi), but also English lately. Some newly created introduced terms from English are not translated yet, and it is more convenient to use them as it is. Proposals to translate them in one or another way were not generally accepted and sound very weird to a native Greek's ears. So the word for computer as υπολογιστής was accepted intelligibly, but to translate the initials CD (compact disk as πηκτός δίσκος !!!), or DVD and USB, no way.
So to conclude with: Which Ancient Greek? More likely the Ancient one of the 5th c. BC in Athens (Attic dialect). But also there is Homer (8th c. BC, a mixture of Ionian and Aeolian dialect, and lyric poets after him, who wrote in Ancient dialects (Ionian and Dorian).
Concerning the Greek Koene that is the language of Gospels, it is the Attic dialect as it was evolved and it is much more closer to the Modern one. So a Modern Greek can understand enough from Gospels, even all with some difficulty of course.
To complete the story: The Ancient Greek as taught in the Departments of Classical Studies in the European and American Universities and some schools there, use the so called Erasmian pronunciation, that is β=b, δ=d etc and the diphthongs οι=oi, αι=ai etc. as the classical scholar Erasmus of Rotterdam proposed: https://en.wikipedia.org/wiki/Erasmus . This pronunciation is not accepted by the Modern Greek scholars, who prefer the Modern Greek way. So it sounds quite bizarre for a Modern Greek to say και as kai. Even so, Ancient Greek is a Classical language, even though it has no other descendant as it happened with Latin. The reason is historical. Modern Greek is the only spoken language that comes from Ancient Greek. And literature written in Ancient Greek is superb! But most manuscripts and works of Ancient Greek were not saved, we only know just a small part of them. I hope, the most important! But this is another story...
We have given a comprehensive review of the Modern Greek alphabet and its pronunciation in the Tips & Notes section in the ABC skill. In addition, you will hear each letter pronounced in the unit one by one and you can hover over the letter to hear it as often as you like. Best wishes. Let us know how you find it.