This book provides a history and analysis of the ideas, problems, concepts, and theories of dimension from ancient to modern times. It focuses primarily on topological and, to a lesser extent, measure-theoretic approaches.

It offers a detailed account of the contributions of key mathematicians who shaped dimension theory, including Bernard Bolzano, Bernhard Riemann, Georg Cantor, Richard Dedekind, Henri Poincaré, L.E.J. Brouwer, Paul Urysohn, Karl Menger, Witold Hurewicz, Paul Alexandroff, and Felix Hausdorff. The book examines the twists and turns in the development of the subject, including its controversies, and explores the philosophical aspects of its history.

As the first in-depth historical study of dimension theory, it serves as a reference for historians and philosophers of mathematics. It also provides general historical background for students and researchers with broader mathematical interests.

Dale Johnson worked for many years at the University of Hertfordshire, UK, where he taught and did research in the history and philosophy of mathematics, publishing papers on Bolzano, Brouwer, and the history of dimension theory. In a second career he contributed research in cybersecurity at The MITRE Corporation, publishing several papers in the field. He is now retired.