This book is based on the lecture notes from a course we taught at Penn
State University during the fall of 2002. The main goal of the course
was to give a complete and detailed proof of the Morse Homology Theorem
(Theo- rem 7.4) at a level appropriate for second year graduate
students. The course was designed for students who had a basic
understanding of singular homol- ogy, CW-complexes, applications of the
existence and uniqueness theorem for O.D.E.s to vector fields on smooth
Riemannian manifolds, and Sard's Theo- rem. We would like to thank the
following students for their participation in the course and their help
proofreading early versions of this manuscript: James Barton, Shantanu
Dave, Svetlana Krat, Viet-Trung Luu, and Chris Saunders. We would
especially like to thank Chris Saunders for his dedication and en-
thusiasm concerning this project and the many helpful suggestions he
made throughout the development of this text. We would also like to
thank Bob Wells for sharing with us his extensive knowledge of
CW-complexes, Morse theory, and singular homology. Chapters 3 and 6, in
particular, benefited significantly from the many insightful conver-
sations we had with Bob Wells concerning a Morse function and its
associated CW-complex.