  In this review the foundations of Geometric Quantization are explained and
discussed. In particular, we want to clarify the mathematical aspects related
to the geometrical structures involved in this theory: complex line bundles,
hermitian connections, real and complex polarizations, metalinear bundles and
bundles of densities and half-forms. In addition, we justify all the steps
followed in the geometric quantization programme, from the standpoint
definition to the structures which are successively introduced.
