I second (third) the recommendations of Lawson-Michelsohn as a primary reference. For a book with less focus on the algebra, you could try "Elliptic operators, topology and asymptotic methods" by John Roe.
There is, however, a couple of Wikipedia entries that you might find interesting.

 - [Lichnerowicz formula][1]
 - [Weitzenböck identity][2]

  [1]: http://en.wikipedia.org/wiki/Lichnerowicz_formula%20%22Lichnerowicz%20formula%22-
  [2]: http://en.wikipedia.org/wiki/Weitzenb%25C3%25B6ck_formula%20%22Weitzenb%C3%B6ck%20identity%22-