Recommended books for Spin Geometry

Question

I would like you to tell me about the best introduction book for spin geometry, in particular, the following topics:

1. Clifford Algebras from the foundation to the classification and their representations.
2. Dirac operator and spinor.
3. Atiyah-Singer Index Theorem, heat kernel and its application to topology and physics.

Once, I consider about "Spin Geometry" by Lawson and Michelsohn, but my knowledge is

1. Geometric topology(homotopy group, (co)homology and K-theory).
2. Differential geometry(Riemannian geometry, de-Rham theory and Hodge theory).
3. Representations for Lie algebras and Lie groups.
4. Functional analysis.

However I have not learned characteristic classes. To read the book of Lawson, is it poor? Should I learn about characteristic classes before index theorem? Or, please tell me another good book. Thank you in advance.

Answer 1

I'm far from an expert on these things, but I think that you might find Andreas Rosén's Geometric Multivector Analysis: From Grassmann to Dirac useful. It starts out with exterior and Clifford algebras, and ends with Atiyah–Singer. At least the parts that I have read so far are very nicely written.