A review of recent developments in the quantum differential calculus. The
quantum group GLqβ(n) is treated by considering it as a particular quantum
space. Functions on SLqβ(n) are defined as a subclass of functions on
GLqβ(n). The case of SOqβ(n) is also briefly considered. These notes cover
part of a lecture given at the XIX International Conference on Group Theoretic
Methods in Physics, Salamanca, Spain 1992.Comment: 23 page