  These notes evolved from the lecture notes of a minicourse given in Swisk,
the Sedano Winter School on K-theory held in Sedano, Spain, during the week
January 22--27 of 2007, and from those of a longer course given in the
University of Buenos Aires, during the second half of 2006. They intend to be
an introduction to $K$-theory, with emphasis in the comparison between its
algebraic and topological variants. We have tried to keep as elementary as
possible.

K-Theory and Homology;Operator Algebras