Handbook of global analysis Global aspects of Finsler geometry T. Aikou and L. Kozma Morse theory and nonlinear differential equations T. Bartsch A. Szulkin and M. Willem Index theory D. Bleecker Partial differential equations on closed and open manifolds J. Eichhorn Spectral geometry P. Gilkey Lagrangian formalism on Grassmann manifolds D.R. Grigore Sobolev spaces on manifolds E. Hebey and F. Robert Harmonic maps F. Helein and J.C. Wood Topology of differentiable mappings K. Houston Group actions and Hilberts fifth problem S. Illman Exterior differential systems N. Kamran Weil bundles as generalized jet spaces I. Kolar Distributions vector distributions and immersions of manifolds in Euclidean spaces J. Korbas Geometry of differential equations B. Kruglikov and V. Lychagin Global variational theory in fibred spaces D. Krupka Second order ordinary differential equations in jet bundles and the inverse problem of the calculus of variations O. Krupkova and G.E. Prince Elements of noncommutative geometry G. Landi De Rham cohomology M.A. Malakhaltsev Topology of manifolds with corners J. Margalef Roig and E. Outerelo Dominguez Jet manifolds and natural bundles D.J. Saunders Some aspects of differential theories J. Szilasi and R.L. Lovas Variational sequences R. Vitolo The Oka Grauert Gromov principle for holomorphic bundles P M. Wong This is a comprehensive exposition of topics covered by the American Mathematical Societys classification Global Analysis dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics. This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics dealing with topics such as; structures on manifolds pseudogroups Lie groupoids and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs differential systems and distributions and spectral theory); variational theory on manifolds with applications to physics; function spaces on manifolds; jets natural bundles and generalizations; and non commutative geometry. Comprehensive coverage of modern global analysis and geometrical mathematical physics Written by world experts in the field Up to date contents Preface Contents 1. Global aspects of Finsler geometry (T. Aikou and L. Kozma) 2. Morse theory and nonlinear differential equations (T. Bartsch A. Szulkin and M. Willem) 3. Index theory (D. Bleecker) 4. Partial differential equations on closed and open manifolds (J. Eichhorn) 5. Spectral geometry (P. Gilkey) 6. Lagrangian formalism on Grassmann manifolds (D.R. Grigore) 7. Sobolev spaces on manifolds (E. Hebey and F. Robert) 8. Harmonic maps (F. Ȟlein and J.C. Wood) 9. Topology of differentiable mappings (K. Houston) 10. Group actions and Hilberts fifth problem (S. Illman) 11. Exterior differential systems (N. Kamran) 12. Weil bundles as generalized jet spaces (I. Kol̀r) 13. Distributions vector distributions and immersions of manifolds in Euclidean spaces (J. Korbas) 14. Geometry of differential equations (B. Kruglikov and V. Lychagin) 15. Global variational theory in fibred spaces (D. Krupka) 16. Second Order Ordinary Differential Equations in Jet Bundles and the Inverse Problem of the Calculus of Variations (O. Krupkov̀ and G.E. Prince) 17. Elements of noncommutative geometry (G. Landi) 18. De Rham cohomology (M.A. Malakhaltsev) 19. Topology of manifolds with corners (J. Margalef Roig and E. Outerelo Dom̕nguez) 20. Jet manifolds and natural bundles (D.J. Saunders) 21. Some aspects of differential theories (J. Szilasi and R.L. Lovas) 22. Variational sequences (R. Vitolo) 23. The Oka Grauert Gromov principle for holomorphic bundles (P M. Wong) A. Abstracts