We demonstrate the construction of the functors K_0 and K_1 , from the category
of C -algebras, to the category of Abelian groups. We define the index map and
we show the isomorphism of the Abelian groups K_0 (SA) and K_1 (A). We proceed
with proving the Bott periodicity and presenting the six-term exact sequence.
Finally, we give some elementary examples of the computation of these groups.
K-Theory, C -algebra, Homomorphism, Functor, Index map