  In this tutorial I intend to present some of the results I obtained through
my PhD work in the "quantum optics group of the University of Isfahan" under
consideration Dr. R. Roknizadeh and Prof. S. Twareque Ali as my supervisor and
advisor, respectively. I will revisit some of the pioneering proposals recently
developed the concept of generalized CSs. As it can be observed the customary
three generalization methods {\it (symmetry, algebraic and dynamical)} have
never been considered in neither of them. Our intention in this work is at
first to investigate the lost ring between the customary three methods and the
recently developed ones, as possible. For this purpose it has been devised
general analytic descriptions, which successfully demonstrate how different
varieties of CSs (which are nonlinear in nature) can be obtained by two
processes, first the {\it "nonlinear CSs"} method and second by {\it "basis
transformations on an underlying Hilbert spaces"}. As a result, I will
systematize the recently introduced generalized CSs in a clear and concise way.
It will be clear also, that how our results can be considered as a first step
in the generation process of the mathematical physics CSs in the context of
quantum optics. Besides this, some new results emerge from our studies. I
introduce a large classes of generalized CSs, namely the {\it "dual family"}
associated with each set of early known CSs. But, in this relation, the
previous processes for constructing the dual pair of Gazeau-Klauder CSs fail to
work well, so I outlined a rather different method based on the {\it "temporal
stability"} requirement of generalized nonlinear CSs.
