Generally speaking, duality theory is concerned with techniques and results which help to establish an equivalence between a category and the dual of a(nother) category. In these notes we give an overview on some of those results, in particular, we describe the structure of dual adjunction, and present several categorical techniques which we find useful for establishing duality results: a Stone-Weierstraß type theorem, limit sketches and pro-completion, and idempotent split completion.