Claudio Gorodski is a Full Professor at the Institute of Mathematics and Statistics, University of São Paulo, Brazil. He holds a PhD in Mathematics (1992) from the University of California at Berkeley, USA, and a Habilitation degree (1998) from the University of São Paulo, Brazil. His research interests include Lie transformation groups in Riemannian geometry, geometry of submanifolds, Riemannian symmetric spaces, and sub-Riemannian geometry.

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• Preface.- Smooth manifolds.- Tensor fields and differential forms.- Lie groups.- Integration.- Appendix A: Covering manifolds.- Appendix B: Hodge Theory.- Bibliography.- Index.

Claudio Gorodski is a Full Professor at the Institute of Mathematics and Statistics, University of São Paulo, Brazil. He holds a PhD in Mathematics (1992) from the University of California at Berkeley, USA, and a Habilitation degree (1998) from the University of São Paulo, Brazil. His research interests include Lie transformation groups in Riemannian geometry, geometry of submanifolds, Riemannian symmetric spaces, and sub-Riemannian geometry.

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• Preface.- Smooth manifolds.- Tensor fields and differential forms.- Lie groups.- Integration.- Appendix A: Covering manifolds.- Appendix B: Hodge Theory.- Bibliography.- Index.