This is a comprehensive exposition of topics covered by the American Mathematical Society's 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. This title features comprehensive coverage of modern global analysis and geometrical mathematical physics. It is written by world-experts in the field. It provides up-to-date contents.