On some systems of real or complex vector fields and their related Laplacians

Our aim is to give a survey of known results (with sometimes new or known ones, but with a simple proof) on some topics about systems of real or complex vector fields and associated Laplacians. We will try to introduce used tools as simply as possible in order to show clearly the connections between the points of views from complex analysis and partial differential equations, focusing on these simple operators. Some results we will mention were obtained in the 60's or 70's, two decades where there was an explosion of new theories on these topics and we will mention some of the numerous papers of that time in this subject, directly connected to questions we are interested in.