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
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