In recent years, many economics and business students have experienced difficulty with the mathematical aspects of their courses. Essential Mathematics for Economics and Business has been written to help students improve their understanding of key mathematical concepts and methods. Assuming no previous background in the subject, this is a user-friendly textbook combining a non-rigorous introduction to mathematics with economic and business applications. The fundamental mathematical concepts are explained as simply and briefly as possible, using a wide selection of Worked Examples, graphs and real-world applications. Few formal proofs are given, in order to avoid overloading students, but plausible explanations of the ideas and theories involved are provided instead. The reader is also made aware of the limitations of mathematics: for instance, that solutions do not always exist. The detailed Worked Examples are followed by extensive Progress and Test Exercises. These provide the necessary drill and practice that students need to succeed at the subject. The Exercises encourage the use of calculators and Microsoft Excel. These electronic aids help students to apply the mathematical methods, plot graphs and calculate tables of data without getting bogged down in excessive and time-consuming detail. Essential Mathematics for Economics and Business does not aspire to instruct mathematicians, but rather to give students who use mathematics a good sense of what is possible and what is reasonable. It has been written as a core textbook for students studying introductory mathematics on a range of degree and diploma courses in economics and business.