  In this Paper we present an approach to Quantum Mechanical Canonical
Transformations. Our main result is that Time Dependent Quantum Canonical
Transformations can always be cast in the form of Squeezing Operators. We
revise the main properties of these operators in regard to its Lie group
properties, how two of them can be combined to yield another operator of the
same class and how can also be decomposed and fragmented. In the second part of
the paper we show how this procedure works extremely well for the Time
Dependent Quantum Harmonic Oscillator. The issue of the systematic construction
of Quantum Canonical Transformations is also discussed along the lines of
Dirac, Wigner and Schwinger ideas and to the more recent work by Lee. The main
conclusion is that the Classical Phase Space Transformation can be maintained
in the operator formalism but the construction of the Quantum Canonical
Transformation is not clearly related to the Classical Generating Function of a
Classical Canonical Transformation. We propose the road of Squeezing Operators
rather than the old one attached to Quantum Operators constructed under the
guideline of the exponential of the Classical Generating Function.
