This post isn’t entirely an excuse to quote from Fiddler on the Roof. I also have long been fascinated with this, well, letter, for lack of a better term. As a child, I would often see this in old books, especially British ones, and wonder about its use and the rules for it. Personally, I’d like to see it make a come-back, but that’s not terribly likely.
(usually written as a digraph or ligature, but also, and in the earliest times, separately ae) was in OE. the symbol of a simple vowel, intermediate between a and e. When short, as in glæd, fæder, it represented orig. Teut. short a, and had the power of modern Eng. a. in man, glad; when long, as in sǽ, flǽsc, the same sound prolonged, as in a common American pronunciation of bear, hair, there. After 1100 the short æ was generally replaced by a (though sometimes by e); the long ǽ continued to be written æ in the 12th and early 13th c., the OE. eá passing into the same sound and symbol, but in the development of ME. this symbol died out, and was replaced by simple e or ee. Thus OE. sǽ, flǽsc, eár, eást are in Ormin and Layamon sæ, flæssh, ær, æst, but afterwards se(e, flesh, ere, eest. The symbol æ, which thus disappeared from the language in 13th c., was re-introduced in 16th c. in forms derived from Latin words with æ, and (this being the Latin symbolization of Greek *) Greek words in *; as ædify, æther. But this æ had only an etymological value, and whenever a word became thoroughly English, the æ or ae was changed into simple e as edify, ether. The æ or ae now remains, only (1) in Greek and Lat. proper names as in Æneas, Cæsar; even these, when familiar, often take e as Judea, Etna; (2) in words belonging to Roman or Gr. Antiquities as ædile, ægis; (3) in scientific or technical terms as ætiology, æstivation, phænogamous, Athenæum; these also when they become popularized take e, as phenomenon, Lyceum, museum, era. Æ initial is thus to be looked upon as an earlier spelling of E, and will here occur only (1) in EE. words that became obsolete, before changing to e, as æ law (OE. ǽ), æ river (OE. eá); (2) in words directly adopted or formed from Latin and Greek which became obsolete before changing to e as ædituate; or have not changed to e because they indicate ancient things as ædile, ægis, or are technical as ægilops, ægrotant, ætiology. All other words will be found under their later form in E.
As to pronunciation usage differs. The analogy of the language, the practice of orthoepists, and the alternate spelling with e, are in favour of æ being treated precisely like e in the same position. But there is a strong tendency with classical scholars (at variance with their practice as to other long L. and Gr. vowels) to make it long (i*) in all positions. This influences popular usage to some extent, so long as æ is written; as soon as e takes its place, natural English habits prevail: cf. æstivate, æstuary, estuary.