Differential geometry and topology
Differential geometry
Basic
Tu, An introduction to manifolds
Lee, Introduction to smooth manifolds
Munkres, Analysis on manifolds
Spivak, Calculus on manifolds
Bishop & Goldberg, Tensor analysis on manifolds
Abraham, Marsden, Ratiu, Manifolds, tensor analysis and applications
Munkres, Analysis on manifolds
Spivak, A comprehensive introduction to differential geometry, vol. 1
Gadea et al, Analysis and algebra on differentiable manifolds
Special subjects
Saunders, The geometry of jet bundles
Vinogradov et al, Symmetries and conservation laws for differential equations of mathematical physics
Krupka, Introduction to global variational geometry
Olver, Applications of Lie groups to differential equations
Olver, Equivalence, invariants and symmetry
Bryant et al, Exterior differential systems
Kruglikov and Lychagin, Geometry of differential equations
Advanced
Mischenko & Fomenko, A short course in differential geometry and topology
Lang, Fundamentals of differential geometry
Spivak, A comprehensive introduction to differential geometry, vols 1-5
Kobayashi & Nomizu, Foundations of differential geometry
Basic differental topology
Guillemin and Pollack, Differential topology
Bott & Tu, Differential forms in algebraic topology
Milnor, Topology from the differentiable viewpoint
Wall, Differential topology
Hirsch, Differential topology
Kosinski, Differential manifolds
Scorpan, The wild world of 4-manifolds
Cobordism
Miller, Notes on cobordism
Stong, Notes on cobordism theory
Freed, Bordism: old and new
Rudyak, On Thom spectra, orientability and cobordism
Surgery
Ranicki, Algebraic and geometric surgery
Wall & Ranicki, Surgery on compact manifolds