The letter æ is a ligature of a and e. In the Middle Ages ligatures and abbreviations were used for various combinations of letters, but only a few of them have survived to the present day, mainly æ and œ.

To write it in HTML as we are doing here, type æ for the lower-case or Æ for the capital.

It is widely seen in Latin, where the diphthongs ae and oe were common, and also in Greek words borrowed via Latin. It was also used in Old English and Old Norse, but in these languages it was a distinct letter, representing a sound that did not occur in Latin.

Old English and Old Norse

In Old English the word for ash tree was written æsc, but pronounced the same as the modern word. Old English also had the ordinary a and e sounds of Latin, so it needed a new letter for this intermediate vowel. In the runic alphabet there was a separate rune for it, and in the Roman alphabet it was represented with the ae-ligature.

It was also used in Old Norse with the same sound, as in Æsir, the gods, those who live in Asgard. In modern Danish and Norwegian, descendants of Old Norse, it is still pronounced roughly the same, or a little closer to e as in bet. (In Swedish it is now written ä.) But in modern Icelandic, which is grammatically almost identical to Old Norse, it has shifted to an "eye" sound.

Latin and Greek

Classical Latin had a diphthong ae, roughly like English "eye", which had developed from a pre-classical sound ai, which to English ears would also be roughly "eye" (as in "aisle"). It also had a diphthong oe. Greek had a diphthong αι, which was borrowed into Latin as ae.

In handwriting, and in italics, which are based on handwriting, the letter a loses its hood and becomes a simple curve: compare a and a. Unfortunately when fused with a following e, the handwritten/italic ae looks virtually identical to the combination oe. Compare:

cælum et pœna
cælum et pœna
(assuming your browsers renders italics correctly... actually, mine doesn't make them similar, oh well.. but if you see them properly printed in a book you'll know what I mean).

In classical Latin ae and oe were quite different diphthongs, but by the mediaeval period they were both pronounced as a long e, and both written and sometimes printed in nearly identical forms. This can lead to confusion about the original Latin vowel. The word for 'sky', caelum, is often mistakenly seen as coelum.

It is recommended that the ligature not be used in writing either Latin words with ae, or borrowings into English such as encyclopaedia, formulae, Caesar, mediaeval. That is a distinctly old-fashioned and un-classical habit. The ligatures were used in the Middle Ages, but not in ancient Rome.

Modern English

Because of the Great Vowel Shift that changed many English sounds around 1400, Latin -ae- normally becomes an "ee" sound in English, as in Caesar and mediaeval. (This is from the mediaeval Latin long e mentioned above.) Most Greek words have come into English via a Latin intermediary, so this applies to them too: Latin encyclopaedia is derived from an original Greek enkuklopaidia.

It is sometimes simplified in spelling to -e-, as (optionally) in encyclopedia and medieval. The same two points apply to -oe-: Croesus "KREE-sus", Oedipus etc. The change of spelling to -e- is more common in the US: esthetic, esophagus for aesthetic, oesophagus.

Of course those last two words illustrate another fact about modern English, that unstressed vowels are often weakened, so we don't use a full "ee" in words like aesthetic. However, the pronunciation "ay" has no historical basis, i.e. was not traditionally used, yet these days you often hear people saying vertebrae as "VERT-e-bray". I recommend "VERT-e-bree". (In real Latin it was "WHERE-teb-rye".)

This letter, now usually called ash in English, is used in the International Phonetic Alphabet to represent the vowel sound in English "ash", the same sound it had in Old English and Old Norse. The spelling aesc is sometimes used.