  A q-deformed version of classical analysis is given to quantum spaces of
physical importance, i.e. Manin plane, q-deformed Euclidean space in three or
four dimensions, and q-deformed Minkowski space. The subject is presented in a
rather complete and selfcontained way. All relevant notions are introduced and
explained in detail. The different possibilities to realize the objects of
q-deformed analysis are discussed and their elementary properties are studied.
In this manner attention is focused on star products, q-deformed tensor
products, q-deformed translations, q-deformed partial derivatives, dual
pairings, q-deformed exponentials, and q-deformed integration. The main concern
of this work is to show that these objects fit together in a consistent
framework, which is suitable to formulate physical theories on quantum spaces.
