This book is intended as a course book in a first course in discrete mathematics. A special aim of the book is to provide an understanding of the role of discrete mathematics in modelling. Phenomena that are modelled are picked from for instance computer science, electronics, and politics. An introductory chapter discusses what is meant by discrete mathe­matics and discrete models, and reviews numeracy,problem solving, and mathematical presentation. Each chapter is started by a summary of the main points that will be covered. The presen­tation is always based on real problems that in a natural way lead to the introduction of the mathe­matical concepts.The text is written in an informal way, with many illustrations and exercises, in most cases with complete solutions. This version in English is a direct translation of the second edition in Swedish, which means that reading instructions intended for the Swedish book can be used for this one without any modification.