  We investigate nonperturbative canonical quantization of two dimensional
dilaton gravity theories with an emphasis on the CGHS model. We use an approach
where a canonical transformation is constructed such that the constraints take
a quadratic form. The required canonical transformation is obtained by using a
method based on the B\"acklund transformation from the Liouville theory. We
quantize dilaton gravity in terms of the new variables, where it takes a form
of a bosonic string theory with background charges. Unitarity is then
established by going into a light-cone gauge. As a direct consequence, black
holes in this theory do not violate unitarity, and there is no information
loss. We argue that the information escapes during the evaporation process. We
also discuss the implications of this quantization scheme for the quantum fate
of real black holes. The main conclusion is that black holes do not have to
violate quantum mechanics.
