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