Analyzes the theory of normed linear spaces and of linear mappings between such spaces, providing the necessary foundation for further study in many areas of analysis. Strives to generate an appreciation for the unifying power of the abstract linear-space point of view in surveying the problems of linear algebra, classical analysis, and differential and integral equations. This second edition incorporates recent developments in functional analysis to make the selection of topics more appropriate for current courses in functional analysis. Additions to this new edition include: a chapter on Banach algebras, and material on weak topologies and duality, equicontinuity, the Krein-Milman theorem, and the theory of Fredholm operators. Greater emphasis is also placed on closed unbounded linear operators, with more illustrations drawn from ordinary differential equations.