In recent years, convex optimization has become a computational tool of central importance in engineering, thanks to it's ability to solve very large, practical engineering problems reliably and efficiently. The goal of this tutorial is to give an overview of the basic concepts of convex sets, functions and convex optimization problems, so that the reader can more readily recognize and formulate engineering problems using modern convex optimization. This tutorial coincides with the publication of the new book on convex optimization, by Boyd and Vandenberghe, who have made available a large amount of free course material and links to freely available code. These can be downloaded and used immediately by the audience both for self-study and to solve real problems.