abstract: We will describe a general theory of Fourier Integral Operators, associated to non necessarily homogeneous canonical transformations. We will insist on a result of differential geometry which allows to define the principal symbol of such operators as a section of a well defined line bundle. That bundle is defined concretely, the base and the bundle itself being subsets of classical groups. In contrast, in the case of homogeneous canonical transformations, Hörmander's theory defines the principal symbol as a section of a bundle abstractly defined by its transition functions. We will show how these bundles can be identified, giving thus an alternative definition of the Maslov bundle.