  We combine the coordinate method and Erlangen program in the framework of
noncommutative geometry through an investigation of symmetries of
noncommutative coordinate algebras. As the model we use the coherent states
construction and the wavelet transform in functional spaces. New examples are a
three dimensional spectrum of a non-normal matrix and a quantisation procedure
from symplectomorphisms. Keywords: Heisenberg group, special linear group,
symplectic group, Hardy space, Segal-Bargmann space, Clifford algebra,
Cauchy-Riemann-Dirac operator, M\"obius transformations, functional calculus,
Weyl calculus (quantization), quantum mechanics, Schr\"odinger representation,
metaplectic representation.
