Graduate Mathematics for Business, Economics and Finance is intended as a textbook for a course in mathematics for master students in business, economics and finance. The language of mathematics is extensively used to analyse problems in economics and finance, and the level of mathematical competence required of graduate students often exceeds that which is taught in undergraduate mathematics courses. This book covers the relevant mathematical models, theories, and methods. The presentation is centred around many worked examples which are written out in full to facilitate understanding of the underlying theory. The author’s aim is to develop both a deep conceptual understanding of the material covered and fluency with the computational techniques. The interested reader will find many proofs often lacking in other textbooks and many relevant applications. The main topics covered are linear algebra, optimization in several variables, differential and difference equations, and systems of differential and difference equations. An appendix provides a short introduction to complex numbers and trigonometric functions. In addition to the large number of worked examples, each chapter includes several problems and exercises.