Two classes of operators are studied that generalize pseudo-differential operators.
Firstly new classes of $\psi$ d. o. with minimal smoothness assumptions are defined in Chapters I and II. The corresponding $L^{2}$ estimates are obtained by new and simple considerations.
Secondly following A. P. Calderon's program, commutators between $C^{1}$ vector fields and classical $\psi$ d. o. are examined. This second class is of special significance. These operators do not belong to the first class and their study requires new methods such as those developed by A. P. Calderon, A. Zygmund and their school (Chap. III and IV).
In Chapter V a conjecture by E. Stein is proved $(S^{-n/2}_{0,0}$ is bounded on $H^{1}$) and in Chapter VI Carleson measures are used for obtaining $L^{2}$ estimates.