Whether you will be an engineer, a physicist or a mathematician, real analysis will be an invaluable tool in your studies. This course will be an advanced introduction to the basic concepts of analysis. You will learn a solid and rigorous theory of basic limits through extensive exercises. We will start with some topology ( open,closed, compact sets and metric spaces) and then switch to limits of sequences (series) and functions. I plan to cover, with plenty of omissions, approximately the first three or four chapters of Rudin's book "Principles of mathematical analysis", which is the standard textbook used in the MIT Real Analysis course. No textbook is required.