Summary: We present in printed form the content of a series of lectures given by the authors at the International Workshop in Classical Analysis held in Yaounde in December. Our purpose is to introduce the problem of \(L^{p,q}\) boundedness of weighted Bergman projectors on tube domains over symmetric cones and show some of the latest progress obtained in this subject. We begin with a complete description of the situation on the upper halfplane. Next we introduce the geometric machinery necessary to study the problem in higher dimensions. This includes the Riemannian structure of symmetric cones the induced Whitney decomposition and the introduction of a wider class of spaces with mixed \(L^{p,q}\) norms. Our main result is the boundedness of the weighted Bergman projector on the weighted mixed norm spaces \(L^{p,q}_{\nu}\) for an appropriate range of indices \(p,q,\nu\). Finally we conclude by discussing various applications further results and open questions.