This text presents an introduction to algebra suitable for upper-level undergraduate or beginning graduate courses. While there is a very extensive offering of textbooks at this level, in my experience teaching this material I have invariably felt the need for a self-contained text that would start ‘from zero’ (in the sense of not assuming that the reader has had substantial previous exposure to the subject), but impart from the very beginning a rather modern, categorically-minded viewpoint, and aim at reaching a good level of depth. Many textbooks in algebra satisfy brilliantly some, but not all of these requirements. This book is my attempt at providing a working alternative.