TITLE: Atiyah-Singer index theorem
QUESTION [54 upvotes]: Every year or so I make an attempt to "really" learn the Atiyah-Singer index theorem.  I always find that I give up because my analysis background is too weak -- most of the sources spend a lot of time discussing the topology and algebra, but very little time on the analysis.  Question : is there a "fun" source for reading about the appropriate parts of analysis?

REPLY [2 votes]: There is a new and attractive book on Index theory and applications to Physics by Booss and Bleecker  which covers all the necessary analysis background. To quote from its preface : 

In order to enjoy reading or even work through Parts I-III, we expect the readerto  be  familiar  with  the  concept  of  a  smooth  function  and  a  complex  separableHilbert  space.   Nothing  more.) 

Note that this is different from the 1984 book 'Topology and Analysis : ASIT and Gauge theoretic Physics' by the same authors which has been mentioned above.