  This is (raw) lecture notes of the course read on 6th European intensive
course on Complex Analysis (Coimbra, Portugal) in 2000. Our purpose is to
describe a general framework for generalizations of the complex analysis. As a
consequence a classification scheme for different generalizations is obtained.
The framework is based on wavelets (coherent states) in Banach spaces generated
by ``admissible'' group representations. Reduced wavelet transform allows
naturally describe in abstract term main objects of an analytical function
theory: the Cauchy integral formula, the Hardy and Bergman spaces, the
Cauchy-Riemann equation, and the Taylor expansion. Among considered examples
are classical analytical function theories (one complex variables, several
complex variables, Clifford analysis, Segal-Bargmann space) as well as new
function theories which were developed within our framework (function theory of
hyperbolic type, Clifford version of Segal-Bargmann space). We also briefly
discuss applications to the operator theory (functional calculus) and quantum
mechanics.
