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

Introduction; Part I. Prologue: The Foundations of Analysis: 1. The axioms of set theory; 2. Number systems; Part II. Functions of a Real Variable: 3. Convergent sequences; 4. Infinite series; 5. The topology of R; 6. Continuity; 7. Differentiation; 8. Integration; 9. Introduction to Fourier series; 10. Some applications; Appendix: Zorn's lemma and the well-ordering principle; Index.

D. J. H. Garling is an 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.