Geometric Discrepancy : An Illustrated Guide 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 exercises and illustrations. In separate more specialized parts it also provides a comprehensive guide to recent research. Including a wide variety of mathematical techniques (from harmonic analysis combinatorics algebra etc.) in action on non trivial examples the book is suitable for a special topic course for early graduates in mathematics and 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 financial mathematics efficient divide and conquer algorithms in computer science etc.). From the reviews: ...The numerous illustrations are well placed and instructive. The clear and elegant exposition conveys a wealth of intuitive insights into the techniques utilized. Each section usually consists of text historical remarks and references for the specialist and exercises. Hints are provided for the more difficult exercises with the exercise hint format permitting inclusion of more results than otherwise would be possible in a book of this size... Allen D. Rogers Mathematical Reviews Clippings (2001) . 1. Introduction 2. Low Discrepancy Sets for Axis Parallel Boxes 3. Upper Bounds in the Lebesgue Measure Setting 4. Combinatorial Discrepancy 5. VC Dimension and Discrepancy 6. Lower Bounds 7. More Lower Bounds and the Fourier Transform A. Tables of Selected Discrepancy Bounds Hints.