This extensively revised and expanded edition of ""Lectures in Differentiable Dynamics"", first published in 1971, provides an authoritative exposition of the central results of this fundamental and rapidly developing mathematical subject, starting from simple engineering systems and proceeding to current research topics concerning differentiable flows on manifolds. The original version of this monograph culminates in the research results of the 1960s, enphasizing the concepts of structural stability and generic dynamics - with references to Morse-Smale and Anosov hyperbolic differential systems.In the new edition there appears a general updating to cover research of the past decade through 1980, with a major supplemental Appendix reviewing the modern developments under five basic areas: nonlinear oscillations, diffeomorphisms and foliations, general theory - dissipative dynamics, general theory - conservative dynamics, and, chaos, catastrophe, and multi-valued trajectories. There is also an extensive bibliography, including special listings of important mathematical conferences, major survey articles, and current research articles.