Let's tackle all of those Greek letters and funny marks over some of them.
We all know the "I am the alpha and the omega", meaning the beginning and the end of all things.
Alpha being the beginning, the first letter of the alphabet, omega being the last. And beta obviously the second, otherwise the alphabet would not be called alphabet but something else altogether. So let's start with these 3 letters and investigate the way the Greeks represent pronunciation and stress (or pitch)

Listen

ἄλφα     βῆτα     ὦ μέγα

What are those funny marks doing on those vowels?
The up and go / over a vowel shows where we stress the word: which syllable, part of the word, is said loúdest and stróngest.
The French always put the stress on the last syllable of a word. Like this:
Americá is a beautifúl countrý.
We say: América is a beaútiful coúntry.
In French, accents are used to tell us how to pronounce the vowels. Acute accent (é) for short and closed sound, grave accent (è) and circumflex (ê) for long and open.
In Spanish, accents show us where the irregular stress falls in a word. Only acute accent is used to indicate stress.
In Portuguese, all 3 accents are used. And, like in ancient Greek, they help us decide
how to pronounce the vowel (open or closed) and
where to put the irregular stress in a word.
Greek (unlike Spanish and Portuguese) has no fixed rules for word-stress, so the stressed syllable is always indicated by some sort of accent-marker - even if there is only one syllable.
All 3 (acute, grave and circumflex) indicate which syllable is to be pronounced loudest, strongest, with the highest pitch. Circumflex ( looking like a small inverted u over the vowel) tells us to draw the sound out long, or pronounce the vowel with voice going up and down again (which makes for a long sound anyway). Both acute and grave are short.

So far so good. But what is that funny little comma-like thing over the
of  ἄλφα  and the
of ὦ μέγα?
It indicates that  α and ω are not preceded by an h sound: arm rather than harm, elbow rather than helbow.
The h sound is indicated by a little c look-alike over the vowel. Little c (being a real letter) stands for h (another real letter):

So	ἄλφα	is	alpha
	ἅλφα	would be	halfa
	ἔλφ	is	elf
	ἕλφ	would be	helf

These two markers are called
two markerssmooth breathing mark (absence of initial h sound) and
two markersrough or aspirated breathing mark (initial h sound)

Α	α	ἄλφα	a, at times short like cup, at times long like rather "long" a is marked in your book with a macron (a small horizontal line over the vowel a) to help you with pronunciation.
Ε	υ	ἒ ψιλόν	e as in get called "plain" or "simple" e (as opposed to the following, rather vulgar e called ἦτα There, what did I say: Three accents: up and go / acute grumpy long ˆ circumflex and gravely bow to thy neighbour \ grave When do we use this grave accent then? If a word stressed on the last syllable is directly followed by another (with no intervening punctuation mark), it becomes all polite and bows its head like so \, gravely. Well, to tell the truth, grave actually means the pitch goes down (like into the grave), so that it can rise again on the following word.
Η	η	ἦτα	ê,  pronounced like French ê or è, or hair or like: daddy, dad, hat rather then het (up), a fad rather than fed up. always longish, sometimes really long, when wearing a had (circumflex). Funny letter, really. Uppercase looks like our H but is pronounced ai, and lowercase looks like an n with a tail hanging down, but is still pronounced ai
Ι	ι	ἰῶτα	at times short i like in spin, at times long i like in queen in your book long i has a little horizontal line, called a macron, over it to show that it is supposed to be pronounced long Note that in Greek we do not dot our i's
Ο	ο	ὂ μικρόν	o called "short o" always short, like in hot
Υ	υ	ὒ ψιλόν	French "u" or German "ü". Make your mouth round like for saying "oo;" in boo, moo, cool and try to say a long "eeeeh" instead.The resulting funny sound should be a good enough approximation of Greek υ try saying:    keel with round lips (as for cool)    mea(sles) with mouth shaped for moo    bean with mouth ready to say boon That's it, approximately, for long υ . For short υ do the same but make it short: Say spin with lips shaped for spoon    tin like it were toon    kin like it were coon
Ω	ω	ὦ μέγα	called "big o" a opposed to the little o we've seen before long open "o" sort of like in automatic, awful, or ohh! in surprise.

Now Diphthongs (di = double, and  φθόγγος = sound):

αι		I am high
αυ		how did the cow plough?
ει		in May my neighbour makes hay
ευ		Gertrude listens to Gershwin eating gherkins
ηυ		like ευ but a bit more vulgar, her with a bit of hair in
οι		a coy boy in a boiler suit
ου		who is in the cool pool?
υι		more or less like: I feel queasy said the twee queen

The interesting thing with diphthongs is that it is the second vowel that has the honour of wearing the diacritic (if there is supposed to be one):
βαί νω 
αὐ τός