This book discusses the intricate realms of geometric function theory and nonlinear potential theory.

This book discusses the intricate realms of geometric function theory and nonlinear potential theory. It offers a distinctive and integrative perspective rooted in the geometric and topological properties of mappings. By synthesizing these foundational concepts, it presents a fresh and accessible approach tailored to researchers and graduate students alike. Key topics include nonsmooth calculus, boundary behavior of functions and the theory of quasiconformal and quasiregular mappings, with practical applications to open-ended analytical problems. The methodologies span a broad spectrum—from real and complex analysis to classical potential theory—underscoring their versatility across mathematical disciplines.

The book establishes a solid foundation for readers eager to pursue independent research in these rapidly evolving fields. Through thoughtfully structured exercises, it offers a rich and engaging learning experience. A carefully curated bibliography supports further exploration, bridging classical foundations with emerging directions in contemporary research. Whether used in classrooms or for self-study, this volume serves as an indispensable resource for those seeking to deepen their understanding and actively contribute to the advancement of mathematical analysis.