This textbook, which originated as a set of lecture notes for a course in geometric topology at Vanderbilt University, and later at Canisius College, is intended for an introductory one semester course in elementary topology, primarily for senior math majors although some portions of it can be used also for sophomores and juniors who have had at least some linear algebra prior to that. The author aims to provide the student with an introduction to the (standard) subjects of point-set topology (neighborhoods, maps, continuity, connectedness, compactness, separation axioms, product and quotient spaces), geometric topology (complexes, triangulation, classification of surfaces, Euler characteristic, graphs, trees), and algebraic topology (covering spaces, fundamental group, cellular homology), and in the end some miscellaneous topics (Jordan curve theorem, 3-manifolds, vector fields on manifolds, integration on manifolds). There are numerous exercises dispersed throughout the text, mostly quite easy, which should be done when they are met (and not at the end). There is also a helpful list of references for further study. The book is written in a very informal, lively style, with lots of illustrations and is a real pleasure to read, proving that it is (still) possible to make a better and more attractive course in elementary topology.