We present a selection of basic results on Borel reducibility of Borel ideals and equivalence relations, especially those with comparably short proofs. The focal point are reducibility/irreducibility results related to some special equivalences like E0,E1,E2,E3,E∞,Z0,
Nearby in the stack
and Banach-induced equivalences
lp,
in particular several dichotomy theorems. The bulk of results included in the book were obtained in the 1990s, but some rather recent theorems are presented as well, like Rosendal's proof that Borel ideals are cofinal within Borel equivalences of general form.