This volume contains lectures from the Conference Board of Mathematical Sciences meeting held at the University of Colorado on May 31June 4, 1976. The lectures consist of an expository discussion of basic results for topological flows and a somewhat more detailed discussion of isolated invariant sets and continuation. The construction of the index for isolated invariant sets is new and allows more general application than previous ones. Also, the index itself is endowed with more structure and the continuation theorem is modified to take this new structure into account. Some elementary applications are given, but the main emphasis is on the abstract theory. Readership Reviews "Every once in a while in mathematics, a strikingly original work appears which radically changes a particular field ... [this book] fits this description, the area being the qualitative theory of nonlinear differential equations."  Mathematical Reviews Table of Contents  On stable properties of the solution set of an ordinary differential equation
 Elementary properties of flows
 The Morse index
 Continuation
 Bibliography
