Author-hosted sample of Chapter 1, Introduction. The second-edition book is credited to John M. Lee, published by Springer in Graduate Texts in Mathematics 202, and carries copyright 2011. Its Chapter 1 definition is explicitly provisional; formal manifold hypotheses in this wiki are supported by the separately cited Toronto notes.
Cited passages: Introduction to Topological Manifolds by John M. Lee, second edition, Chapter 1, pages 1–3 on local models and pages 5–6 on topological invariants.