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Non-Gaussianity and extragalactic foregrounds to the Cosmic Microwave Background

[Abridged] This PhD thesis was defended in September 2013 at Université Paris-Sud, France. It studies the non-Gaussianity (NG) of extragalactic foregrounds to the Cosmic Microwave Background (CMB). This is particularly important for the analysis of CMB data from the Planck satellite, in which I was involved. I studied in particular the extragalactic foregrounds tracing the Large Scale Structure (LSS) of the universe : radio and infrared point-sources and the thermal Sunyaev-Zel'dovich effect (tSZ). The motivations and summary of this thesis cannot be shortened into the length constraints of this abstract and are thus described in an inner abstract and introduction. In a broad summary, this thesis is organised in the following parts : statistics of random variables and fields, spherical analysis in particular of polyspectra, some cosmology (inflation and its NG, CMB, LSS and halo model), extragalactic foregrounds (tSZ, point-sources), and measuring the NG of these foregrounds with Planck. More specifically and in a disorganised manner, the following were most of my contributions in the field : developments on the effect of masking on the angular bispectrum, introduction of an efficient bispectrum representation, derivation of the bispectrum covariance, generation of non-gaussian simulations, projection of 3D Fourier polyspectra onto 2D spherical ones, treatment of shot-noise terms with the halo model, introduction of a diagrammatic formalism for elegant and simple derivation of galaxy polyspectra, halo model description of the bispectrum of the tSZ effect and of the Cosmic Infrared Background (CIB), phenomenological prescription of the NG of clustered sources and corresponding KSW-like estimator, effect of point-sources NG for Planck, measurement of the CIB bispectrum with Planck data, measurement of the tSZ bispectrum with Planck data and cosmological constraints with it.