The main text of this volume presents a partly new approach to the microlocal analysis of analytic singularities based on an idea of Bros-Iagolnitzer and on the use of complex phase functions. Topics such as the stationnary phase method, resolu-tions of the identity, propagation of singularities and higher order microlocalisa-tions are discussed. In section 11 we developp the germ of what will hopefully be-come a very general approach to Fourier integral operators.
The second text illustrates how similar techniques can be applied to problems in the $C^{\infty}$-theory. Here we construct the exponential of operators with multiple cha-racteristics and obtain a result on the propagation of singularities for such operators.