  This article provides a basic introduction to some concepts of
non-commutative geometry. The importance of quantum groups and quantum spaces
is stressed. Canonical non-commutativity is understood as an approximation to
the quantum group case. Non-commutative gauge theory and the non-commutative
Standard Model are formulated on a space-time satisfying canonical
non-commutativity relations. We use *-formalism and Seiberg-Witten maps.
