We define topological manifolds and topological manifolds with boundary. Then we introduce coordinate charts and atlases. Finally, we discuss how one would use topological invariants to prove invariance of dimension and invariance of boundary. 00:00 Introduction 00:16 Some spaces that may be manifolds 11:05 Definition: Locally Euclidean Spaces 16:24 Definition: Topological Manifold 19:42 Charts and Atlases for Manifolds 24:36 Thm: Invariance of Dimension 32:19 Motivation: Manifolds with Boundary 33:01 Definition: Upper Half-space 34:17 Definition: Topological Manifold with Boundary 40:38 Thm: Invariance of Boundary This lecture follows Lee's "Introduction to topological manifolds", chapter 2. A playlist with all the videos in this series can be found here:    • Topology