Explore advanced mathematical concepts in this graduate-level lecture on Analysis on Manifolds, presented in Portuguese by Professor Vinicius Ramos at the Instituto de Matemática Pura e Aplicada (IMPA). Building upon prerequisites in Rn Analysis, delve into differentiable manifolds, manifolds with boundary, and orientable manifolds. Master partition of unity and Whitney's embedding theorem for compact manifolds. Study tangent and cotangent bundles, differential applications, regular values, alternating forms, differential forms, and exterior derivatives. Learn about surface integrals, Stokes' theorem, De Rham cohomology, Mayer-Vietoris sequence, homotopy invariance, vector fields as sections and derivations, tensors, and their applications. Based on foundational texts by Lima, Spivak, and Tu, gain comprehensive understanding of advanced mathematical analysis through rigorous theoretical exploration and practical applications.