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Summary form only given. The strong coupling between quantum well excitons and cavity photons leads to the appearance of a new type of quasi-particles, the so-called microcavity polaritons. The energy dispersion of polaritons is very sharp owing to the photon component. At the same time, the polaritons are strongly interacting due to the exciton-exciton interaction and saturation. In this contribution, we present a microscopic theory for the nonlinear optics of the polariton matter: microscopic equations are presented for two different regimes. The first regime concerns the coherent angle-resolved pump-probe spectroscopy. We demonstrate that a parametric process leads to a giant angle-resonant amplification of the probe beam in very good agreement with recent experiments. Analytical and numerical results show that the amplification has a threshold in the dependence on the pump intensity. The threshold intensity is such that the lower polariton blueshift is equal to its linewidth.