What is the "most uniform" way of distributing n points in the unit square? How big is the "irregularity" necessarily present in any such distribution? Such questions are treated in geometric discrepancy theory. The book is an accessible and lively introduction to this area, with numerous illustrations and exercises. In separate, more specialized parts, it also provides a comprehensive guide to recent research in the field. Including a wide variety of mathematical techniques (from harmonic analysis, combinatorics, algebra, etc.) in action on nontrivial examples, the book is suitable for a "special topic" course for early graduate students in mathematics and in computer science. Besides professional mathematicians, it will be of interest to specialists in fields where a large collection of objects should be "uniformly" represented by a smaller sample (such as high-dimensional numerical integration in computational physics or in financial mathematics, efficient divi! de-and-conquer algorithms in computer science, and others).