This is an introductory textbook of linear programming, written mainly for students of computer science and mathematics. Our guiding phrase is, "what every theoretical computer scientist should know about linear programming". The book is relatively concise, in order to allow the reader to focus on the basic ideas. For a number of topics commonly appearing in thicker books on the subject, we were seriously tempted to add them to the main text, but we decided to present them only very briefly in a separate glossary. At the same time, we aim at covering the main results with complete proofs and in sufficient detail, in a way ready for presentation in class. One of the main focuses is applications of linear programming, both in practice and in theory. Linear programming has become an extremely—- ible tool in theoretical computer science and in mathematics. While many of the finest modern applications are much too complicated to be included in an introductory text, we hope to communicatesome of the—avor (and excitement) of such applications on simpler examples.