A reference for studying spinors from a mathematical point of view I need to know spinors in terms of mathematics. Does anybody know a good reference for that purpose? I am familiar with spinor algebra but its mathematical perspective still is not clear to me.
 A: Lawson and Michelsohn, Spin Geometry, is perhaps the standard mathematical reference, and an excellent book.
A: As Ben McKay already mentioned, Spin Geometry by Lawson and Michelsohn is a great reference.
I want to add a few other references (in no particular order) that all include an introduction to the basic concepts of spin geometry (Clifford algebras and their representations, spin groups, spin structures, spinor bundles).


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*Dirac Operators in Riemannian Geometry by Thomas Friedrich

*Elliptic operators, topology and asymptotic methods by John Roe

*A Spinorial Approach to Riemannian and Conformal Geometry by J.-P. Bourguignon, O. Hijazi, J.-L. Milhorat, A. Moroianu, S. Moroianu. This is a fairly recent book. 

*Spectral Properties of the Dirac Operator and Geometrical Structures by O. Hijazi. This appeared in Proceedings of the Summer School on Geometric Methods in Quantum Field Theory, Villa de Leyva, Colombia, July 12-30, (1999), World Scientific 2001

*The Dirac Spectrum by N. Ginoux. 

