  The essentials of a new method in solving very large classes of nonlinear
systems of PDEs, possibly associated with initial and/or boundary value
problems, are presented. The PDEs can be defined by continuous, not necessarily
smooth expressions, and the solutions obtained cab be assimilated with usual
measurable functions, or even with Hausdorff continuous ones. The respective
result sets aside completely, and with a large nonlinear margin, the celebrated
1957 impossibility of Hans Lewy regarding the nonexistence of solution in
distributions of large classes of linear smooth coefficient PDEs.
