The second volume of three providing a full and detailed account of undergraduate mathematical analysis.

Introduction; Part I. Metric and Topological Spaces: 1. Metric spaces and normed spaces; 2. Convergence, continuity and topology; 3. Topological spaces; 4. Completeness; 5. Compactness; 6. Connectedness; Part II. Functions of a Vector Variable: 7. Differentiating functions of a vector variable; 8. Integrating functions of several variables; 9. Differential manifolds in Euclidean space; Appendix A. Linear algebra; Appendix B. Quaternions; Appendix C. Tychonoff's theorem; Index.

D. J. H. Garling is Emeritus Reader in Mathematical Analysis at the University of Cambridge. He has 50 years' experience of teaching undergraduate students in most areas of pure mathematics, but particularly in analysis.