Geometric Discrepancy Theory

This volume offers a systematic introduction to geometric discrepancy theory, rooted in a series of open problems that drive current research. Based on the author's invited talk Results and Problems Old and New in Discrepancy Theory at the Special Semester on Multivariate Algorithms and their Foundations in Number Theory at RICAM, Austria, this book presents the foundational results leading up to these open questions while providing a guided pathway for further investigation.Designed to be almost self-contained, it requires only basic knowledge of number theory, probability, and analysis. The book emphasizes clarity and accessibility, making it suitable for both beginning graduate students and experienced researchers seeking a structured entry into geometric discrepancy theory.