A fresh approach to topology makes this complex topic easier for students to master. Topology-the branch of mathematics that studies the properties of spaces that remain unaffected by stretching and other distortions-can present significant challenges for undergraduate students of mathematics and the sciences. Understanding Topology aims to change that. The perfect introductory topology textbook, Understanding Topology requires only a knowledge of calculus and a general familiarity with set theory and logic. Equally approachable and rigorous, the book's clear organization, worked examples, and concise writing style support a thorough understanding of basic topological principles. Ault's unique emphasis on fascinating applications, from mapping DNA to determining the shape of the universe, will engage students in a way traditional topology textbooks do not. This groundbreaking new text: presents Euclidean, abstract, and basic algebraic topology explains metric topology, vector spaces and dynamics, point-set topology, surfaces, knot theory, graphs and map coloring, the fundamental group, and homology includes worked example problems, solutions, and optional advanced sections for independent projects Following a path that will work with any standard syllabus, the book is arranged to help students reach that "Aha!" moment, encouraging readers to use their intuition through local-to-global analysis and emphasizing topological invariants to lay the groundwork for algebraic topology.