FM 97-4 Author: G. Gallavotti Title: Breakdown and regeneration of time reversal symmetry in nonequilibrium Statistical Mechanics Abstract: A review and non technical exposition of recent studies on the relevance of time reversal, on its spontaneous breakdowns, and on its possible resurgence as a weaker symmetry that still anticommutes with time evolution. Comment: A review talk given at the meeting in honor of Raoul Gatto, Ginevra, 17 jan 1997. Keywords: Time reversal, Reversibility, Irreversibility, Chaos, Nonequilibrium, Statistical Mechanics, Dynamical Systems Fisica, Universita' di Roma La Sapienza, P.le Moro 2, 00185, Roma, Italia. e-mail giovanni@ipparco.roma1.infn.it tel. 6-49914370, fax 6-4957697