Book excerpt: "The book is highly recommended as a text for an introductory course in nonlinear analysis and bifurcation theory... reading is fluid and very pleasant... style is informal but far from being imprecise." -review of the first edition. New to this edition: additional applications of the theory and techniques, as well as several new proofs. This book is ideal for self-study for mathematicians and students interested in geometric and algebraic topology, functional analysis, differential equations, and applied mathematics.