|Contents: Irreversibility; Quantum irreversibility; Stochastic dynamics: irreversibility from coarse graining; . Initial conditions vs. ﬁnal conditions: a restatement of the second law; . Arrows of time; . Correlating arrows of time; . The universe with two-time boundary conditions; How do you deﬁne macroscopic? . . . with practical consequences; Coarse grains; Quantum measurement theory; Quantum measurement theory.