When do I use æ?

Solution 1:

It is an ancient grapheme sometimes used in literary/historical contexts. I don’t think you will need to use it in current common language.

Æ (minuscule: æ) is a grapheme named æsc or ash,*** formed from the letters a and e, originally a ligature representing the Latin diphthong ae.

In English æ is often eschewed in favour of the digraph ae. Usage experts often consider that incorrect, especially for foreign words in which æ is considered a letter (such as Æsir, Ærø) or brand names that use the ligature or a variation of it (such as Æon Flux, Encyclopædia Britannica, Ætna, Inc.).

Given their long history, ligatures are sometimes used to invoke archaism or in literal quotations of historic sources; for instance, words such as dæmon or æther are often treated so.

(Wikipedia)