  The purpose of this paper is to introduce several basic theorems of coherent
states and generalized coherent states based on Lie algebras su(2) and su(1,1),
and to give some applications of them to quantum information theory for
graduate students or non--experts who are interested in both Geometry and
Quantum Information Theory. In the first half we make a general review of
coherent states and generalized coherent states based on Lie algebras su(2) and
su(1,1) from the geometric point of view and, in particular, prove that each
resolution of unity can be obtained by the curvature form of some bundle on the
parameter space. In the latter half we apply a method of generalized coherent
states to some important topics in Quantum Information Theory, in particular,
swap of coherent states and cloning of coherent ones. We construct the swap
operator of coherent states by making use of a generalized coherent operator
based on su(2) and show an "imperfect cloning" of coherent states, and moreover
present some related problems. In conclusion we state our dream, namely, a
construction of {\bf Geometric Quantum Information Theory}.
