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. A highlight of the second edition is 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. Other highlights include topics that have applications to both linear and nonlinear functional analysis, extended coverage of the uniform boundedness theorem, and plenty of exercises with solutions provided at the back of the book.