  This survey paper is an expanded version of lectures given at the Clay
Mathematics Academy ; see
http://www.claymath.org/programs/outreach/academy/colloquium2005.php These
lectures were intended to very young (and motivated) college students with
little background. Therefore, they are accessible to a mathematician of any
speciality willing to understand the subject. A much more complete introduction
to K-theory may be found in the "Handbook of K-theory", recently edited by
Springer.
