This video course supports the Fall 2025 MTH675 class at Oregon State University. The material from this video can be found in the books: Lee, John M. Introduction to smooth manifolds. Second edition. Grad. Texts in Math., 218 Springer, New York, 2013. xvi+708 pp. Boothby, William M. An introduction to differentiable manifolds and Riemannian geometry. Second edition. Pure Appl. Math., 120 Academic Press, Inc., Orlando, FL, 1986. xvi+430 pp. Tu, Loring W. An introduction to manifolds. Second edition. Universitext Springer, New York, 2011. xviii+411 pp. This video was animated using the Manim extension of Python, developed by the Manim community, and originally created by Grant Sanderson: Music: Reaching Out - Anna Landstrom Watching Her Paintings - Franz Gordon Winter Dreams - Megan Wofford If You Say Yes - Anna Landstrom Ever After - William Claeson Blushing - Magnus Ludviggson