In this talk, I will report the first part of my paper(Projections  in several complex variables, Mem. Soc. Math. France, 2010, 131 p.). In this work, we completely study the heat equation method of Menikoff-Sjostrand and  apply it to the Kohn Laplacian defined on a compact orientable connected CR manifold. We then get the full asymptotic expansion of the Szego projection for (0, q) forms when the Levi form is non-degenerate. This generalizes a result of Boutet de Monvel and Sjostrand for (0,0) forms.