Introduction to Differentiable Manifolds provides a clear and thorough introduction to modern differential geometry. The text methodically lays the groundwork by defining differentiable manifolds and their tangent spaces, and it guides readers through both Euclidean and abstract viewpoints. Early chapters develop the essential structures through carefully selected examples, while later sections explore the role of differential structures in various contexts. Continuing into the advanced topics, the book examines the construction of tangent bundles and the behavior of vector fields, linking these ideas to ordinary differential equations. A lucid treatment of Lie group theory is presented, including the fundamental relationship between Lie subalgebras and Lie subgroups. Supplemented with a wealth of exercises and illustrative examples, this work is ideally suited for readers with a background in finite-dimensional vector spaces, point-set topology, and advanced calculus.
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