The Second Edition of this successful text offers a systematic exposition of the basic ideas and results of Hilbert space theory and functional analysis. It includes a simple introduction to the Lebesgue integral and a new chapter on wavelets. The book provides the reader with revised examples and updated diverse applications to differential and integral equations with clear explanations of these methods as applied to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation.