This book is a self-contained treatment of all the mathematics needed by undergraduate and masters-level students of economics. Building up gently from a very low level, the authors provide a clear, systematic coverage of calculus and matrix algebra. The second half of the book gives a thorough account of optimisation and dynamics in discrete and continuous time. The final two chapters are an introduction to the rigorous mathematical analysis used in graduate-level economics. The emphasis throughout is on intuitive argument and problem-solving. All methods are illustrated by well-chosen examples and exercises selected from central areas of modern economic analysis. The book's careful arrangement in short chapters enables it to be used in a variety of course formats for students with and without prior knowledge of calculus, as well as for reference and self-study. New features of the third edition include: > sections on double integration and dynamic programming; > substantial rewriting and expansion of early chapters, making the book highly accessible for the complete beginner. > answers to all exercises and full solutions to all problems are available free online at