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Lectures on the Geometry of Manifolds
This book introduces the reader to the concept of smooth manifold through abstract definitions and, more importantly, through many we believe relevant examples. Topics covered includes: Manifolds, Natural Constructions on Manifolds, Calculus on Manifolds, Riemannian Geometry, Elements of the Calculus of Variations, The Fundamental group and Covering Spaces, Cohomology, Characteristic classes, Classical Integral Geometry, Elliptic Equations on Manifolds and Dirac Operators.
Author(s): Liviu I. Nicolaescu
570 Pages 
Introduction to manifolds by M Lubke
This note covers submanifolds of Euclidean space, Differentiable manifolds, Differential forms, Integration on manifolds.
Author(s): M Lubke
92 Pages
Lectures on the Geometry of Manifolds
This book introduces the reader to the concept of smooth manifold through abstract definitions and, more importantly, through many we believe relevant examples. Topics covered includes: Manifolds, Natural Constructions on Manifolds, Calculus on Manifolds, Riemannian Geometry, Elements of the Calculus of Variations, The Fundamental group and Covering Spaces, Cohomology, Characteristic classes, Classical Integral Geometry, Elliptic Equations on Manifolds and Dirac Operators.
Author(s): Liviu I. Nicolaescu
570 Pages