Vowels exist in all words in English. They're a primary functional part of pronunciation, and like all letters in English usually have two or three forms of expression when pronounced, the phonetic pronunciations and the 'capital' pronunciation and an articulated pronunciation which varies depending on the the word. Some vowels are modified depending on the word involved. It should be noted that American and English pronunciation differs in use of some vowels. Vowels may be pronounced differently in some cases, but are still correct pronunciation for that usage. (The classic case is the Anglo/American pronunciation of 'tomato', either Anglo Tomahto or American Tomayto.)
Please note that vowels interact in English and modify the usage of other vowels in pronunciation.
The letter A's pronunciation can vary considerably, particularly when it's the first letter of a word. A word like 'radar' Ray-dah has two forms of pronunciation.
A is pronounced as a short form lower case 'a' as in apple, 'ar/ah' as in argue, 'Ay', the capital form, as in ace, or 'aw' as in awe with irregular exceptions. The capital pronunciation is normally used before nouns Proper names starting with A vary, but are usually the short 'a'.
'a': actor, acceptable, additive, aversion, ant, allegory, ample, antonym, angular, ancestry, aberration, algorithm, agistment, agitate, an, ajudicate, amend, apt, appropriate, ancillary.
'ar/ah': 'ar' words make the 'a' effectively silent, using the capital R as the pronunciation. These words often modify the vowel with the letter after the 'a'. 'ah' is also used in sentences in preference to the capital pronunciation. Both are correct, in most cases. For example, 'A tree' can be pronounced 'A' tree, 'Ah' tree, or 'Ay' tree.
argue, arbitrate, arm, aria, are, arc, art, argument, hard, heart, hearth, harness, hark, bark, large, aardvaark, garden, guard, garment garner (double a's are always 'ah'.)
(A 'rr' usually means the a is pronounced 'a'. as in arrogance, arrangement, arrest, etc.).
Depending on usage and culture, the short 'a' and the 'ar/ah' can often be interchanged. A word like amend can be pronounced amend or ahmend. Variables: (Can be either Anglo 'ah' or American 'ay' or 'a') half, after, rather, etc.
This is the pure vowel sound, used in grammar and sentence construction as the default singular expression. The pronunciation of the letter on its own is emphasized to refer to a single object or state.
aim, amiable, ail, angel, ale, mail, male, sale, pale, rain, drain, stain, wane, strange, deranged, estranged.
As you can see, some pronunciations of vowels like A have regular, common bases in their words. These are usually reliable pronunciations in all cases.
E is pronounced 'ee' for the capital E, 'eh' or 'er' in the shortened form.
'ee' can be the capital form, or a usage of the letter:
era, eradicate, easel, egalitarian. elope, erase, eve, even.
Note that a word with e(consonant)e as its structure is usually pronounced as 'ee'.
Note: Due to usage, many words which are nominally 'ee' words can be pronounced 'eh' or 'er'.
'eh' or 'er' words: eventually, every,
Effect on pronunciation: In various words the use of E on the end of a word often, but not always, modifies the pronunciation of other vowels into their capital form:
ate, equate, sale, sole, quite, quote, cute, mite, mote, dote, white, site, rite, etc. Note that the E is actually silent with a preceding vowel in these cases. Unlike other languages, the single E at the end of a word usually isn't enunciated. If pronounced, it's usually spelled with a double E, like franchisee. Anglicized versions of foreign words may use the foreign pronunciation.
However, usage has a role in some pronunciations. There are exceptions, notably the ..ble words, where the short form of the preceding vowel is used.
able follows the rule, but amiable doesn't.
Spelling forms of E:
ie and ei: auntie, receive, niece, piece se: serial, season, sea, usually pronounced like C, with exceptions. ae: the Greek E, either 'eh' or E: aesthetic, aeon, Aesop. ea: Always an E like easy, eat, ear, eagle y in the end of a word: Usually pronounced as an e with adverbs and names: Jenny, Benny, quickly, thickly, any, many
II is pronounced 'ai' as in 'eye' as the capital or 'i' as in 'it' as the lower case.
'Ai': Aisle, idyll, iron, island, line, irony, 'i' in, important, impetuous, if, ignorant, incessant, irregular, link, stink, think
OO is pronounced as 'owe' the capital form or 'oh'.
U is pronounced like 'You' as the capital, 'uh' as the lower case, or modified by Q or other vowels.'You' usual, university, useful, user, unify