Translator’s Preface to J. Milnor’s book ″Morse Theory″

Abstract

Milnor’s book is a textbook on Morse theory. Starting with the simplest example and finishing with Bott’s Periodicity theorem, the exposition remains geometrically intuitive but rigorous. It is modern but also elegant; it is extensive but also self-contained: the necessary facts from differential geometry, calculus of variations, and so on, are derived in the book itself in a form required by the author.