  A detailed account of the construction of a homogeneous space for the quantum
"az+b" group is presented. The homogeneous space is described by a commutative
C*-algebra which means that it is a classical space. Then a covariant
differential calculus on the homogeneous space is constructed and studied. A
covariant measure and an analogue of the exponential function are used to
introduce elements of Fourier analysis.
