This is an undergraduate introduction to functional analysis, with minimal prerequisites, namely linear algebra and some real analysis It is extensively cross referenced, has a good index, a separate index of symbols Very Good Feature , and complete solutions to all the exercises It has numerous examples, and is especially good in giving both examples of objects that have a given property and objects that do not have the property Allen Stenger, MathDL, April, This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite dimensional linear algebra can be extended or generalized to infinite dimensional spaces Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis including the theory of metric spaces , and Lebesgue integration, although an introductory chapter summarizes the requisite material Highlights of the second edition include a new chapter on the Hahn Banach theorem and its applications to the theory of duality This chapter also introduces the basic properties of projection operators on Banach spaces, and weak convergence of sequences in Banach spaces topics that have applications to both linear and nonlinear functional analysis extended coverage of the uniform boundedness theorem plenty of exercises, with solutions provided at the back of the book