Ancient Greek Phonology

I just started studying Ancient Greek at school and am puzzled by a number
of things in the pronunciation guide of my study book (such guides are
always very vague and overall abominable to the phonetically conscious). I
do not attend class (I am on a self-study program) so it's not easy for me
to ask my teacher. But she probably wouldn't understand my question
anyway...

Of course, I could go to the library to look for answers, but hey, it's more
fun to ask you guys :)

Now, in an attempt to construct a vowel system from the data in the book, I
get this:

(disregarding phonemic vowel length, which applies to all the vowels)

  /i/ /y/
     \
     /e/
       \   /O/
       /A/

Obviously, this is not a symmetrical vowel system. What's up with that?
Why's there no /u/ or /o/? This doesn't seem natural. I'm finding it hard to
believe that my book is not mistaken or that I haven't misunderstood my book
somehow (despite reading it over multiple times). Also, how come /y/ 'y
psilon' has been rendered as either 'y' or 'u' in English (and probably
Latin)?

There has to be, as always, a simple answer to this all, making my question
silly. There must be lots of AG-connosseurs on this list, now give me your
best shot :)

Óskar
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