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Preface
Acknowledgments
1 Basic Notions and Concepts
1£®1 Metric Spaces
1£®2 Linear Algebra
1£®3 The Derivative
1£®4 the Inverse and Implicit Function Theorems
1£®5 the Riemann Integral
1£®6 Improper Integrals
1£®7 The Change of Variable theorem

2 Manifolds
2£®1 Smooth Manifolds
2£®2 The Tangent and Cotangent Bundles
2£®3 Stokes' Theorem
2£®4 Applications of Stokes' Theorem

3 Riemannian and Pseudo-Riemanruan Geometry
3£®1 The Pseudo-Riemannian Measure
3£®2 Connections
3£®3 The Levi-Civita Connection
3£®4 Geodesics
3£®5 the Jacobi Operator
3£®6 the Gauss-Bonnet Iheorem
3£®7 The Chern-Gauss-Bonnet Iheorem

Bibliography
Authors' Biographies
Index
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