  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 $E_0, E_1, E_2, E_3, E_\infty, Z_0,$ and Banach-induced
equivalences $l_p,$ 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.
