  This is an expository paper which gives a proof of the Atiyah-Singer index
theorem for Dirac operators, presenting the theorem as a computation of the
K-homology of a point. This paper and its follow up ("K-homology and index
theory II: Elliptic Operators") was written to clear up basic points about
index theory that are generally accepted as valid, but for which no proof has
been published. Some of these points are needed for the solution of the
Heisenberg-elliptic index problem in our paper "K-homology and index theory on
contact manifolds" Acta. Math. 2014.
