The book contains an exposition of S. Smale's famous theorem on h-cobordism and its applications to important differential topology problems. The book is written in clear, accessible language and can serve as an excellent introduction to cobordism theory and to some extent to general differential topology. Therefore, this monograph is of interest not only for topologists, but also for mathematicians of other specialties. It will be useful for senior students, graduate students and teachers of universities and pedagogical institutes.