This is the new edition of Serge Langs Differential and RiemannianManifolds. This text provides an introduction to basic concepts indifferential topology differ... » 

This is the new edition of Serge Langs Differential and RiemannianManifolds. This text provides an introduction to basic concepts indifferential topology differential geometry and differential equations andsome of the main basic theorems in all three areas for instance theexistence uniqueness and smoothness theorems for differential equations andthe flow of a vector field the basic theory of vector bundles including theexistence of tubular neighborhoods for a submanifold the calculus ofdifferential forms basic notions of symplectic manifolds including thecanonical 2form sprays and covariant derivatives for Riemannian and pseudoRiemannian manifolds applications to the exponential map including theCartanHadamard theorem and the first basic theorem of calculus of variations. «