To learn about geometry and manifolds, I recommend Experiencing Geometry by Henderson. In this book, you can explore a different kind of learning where the reader is asked questions to stimulate their own ideas of how to define constructs and solve problems leading towards key concepts.
"A Guide to the Classification Theorem for Compact Surfaces" by Gallier and Xu provides an in depth explanation and a good introduction to the classification theorem.
Fleischmann, Yael. "A Geometric Approach to Classical Lie Algebras.'' Eindhoven University of Technology, 2015.
"Geometric 2-Manifolds." Experiencing Geometry: in Euclidean, Spherical, and Hyperbolic Spaces, by David W. Henderson and Daina Taimina, Prentice Hall, 2001, pp. 245–266.
Levine, Maxwell. “GLn(R) AS A LIE GROUP.” 21 Aug. 2009, http://www.math.uchicago.edu/~may/VIGRE/VIGRE2009/REUPapers/Levine.pdf.
Marsh, Adam. "Manifold Properties of Matrix Groups." Mathematics for Physics, An Illustrated Handbook, World Scientific Publishing, 2018, \www.mathphysicsbook.com/mathematics/lie-groups/matrix-groups/manifold-properties-of-matrix-groups/.
“Simple Lie Group.” Wikipedia, Wikimedia Foundation, 14 Apr. 2021, en.wikipedia.org/wiki/Simple_Lie_group#Exceptional_cases.
Tapp, Kristopher. Matrix Groups for Undergraduates. 2nd ed., American Mathematical Society, 2016.