Introduction -- Chapter I Homogeneous functions, Fourier transformation, and contact structures -- 1. Integration on manifolds -- 2. Analysis on RPn and smooth homogeneous functions on R*n+1 -- 3. Homogeneous and formally homogeneous distributions -- 4. Fourier transformation of homogeneous functions -- 5. Homogeneous symplectic and contact structures -- 6. Functorial properties of the phase space and local representation of Lagrangian manifolds. The classification lemma -- Chapter II Fourier-Maslov operators -- 1. Maslov's canonical operator (R*-equivariant theory) -- 2. Fourier-Maslov integral operators -- 3. Singularities of hyperbolic equations -- examples and applications -- Chapter III Applications to differential equations -- 1. Equations of principal type -- 2. Microlocal classification of pseudodifferential operators -- 3. Equations of subprincipal type -- References -- Index.