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I am looking for some introductory book/paper/notes about the several index theorems and their applications. By several I mean the "classical" Atiyah-Singer theorem, the local index theorem (APS) and the index theorems for families (Including Bismut's approach). I am less interested in the different proofs but rather on the setup for each result.

Thanks

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    $\begingroup$ The books by Berline–Getzler–Vergne, Booss–Bleecker, and Shanahan all offer introductions to the index theory from different viewpoints. $\endgroup$ Oct 28 '20 at 15:29
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Atiyah's expository paper, "Algebraic Topology and Elliptic Operators", Communications in Pure and Applied Mathematics 20 (1967) 237-249 is quite accessible.

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