This book draws on elements from everyday life, architecture, and the arts to give the reader elementary notions of geometric topology. Pac Man, subway maps, and architectural blueprints are the starting point for exploring how knowledge about geometry and, more specifically, topology has been consolidated over time, offering a learning journey that is both dense and enjoyable. The text begins with a discussion of mathematical models, moving on to Platonic and Keplerian theories of explanation of the Cosmos. Geometry from Felix Klein's point of view is then presented, as a path to an introduction to topology. The final chapters present the concepts of closed, orientable, and non-orientable surfaces, and models of hypersurfaces. With a style that is both rigorous and accessible, this work will be of interest to a broad audience, from curious students and researchers in various areas of knowledge to everyone who feels instigated by the power of mathematics in representing our world - and beyond.

Ton Marar is an Associate Professor at the Institute of Mathematics and Computer Sciences, University of São Paulo at São Carlos, Brazil. He holds a Master's degree (1983) in Mathematics (Geometry) from the same university, and a PhD (1989) from the University of Warwick, United Kingdom. His research fields include singularity theory and geometric topology or, more specifically, geometry and classification of singular surfaces and geometric aspects of singularities of maps.