In the submitted scientific monograph, the developed method of optical detection and analysis of geometric parameters of the topography of abrasive waterjet cut wall surfaces for proposing a method of automatic quality check and control is presented. On the basis of analysis and interpretation of data obtained from the surface, a topography function Rad, which is necessary to be known for the subsequent prediction and control of abrasive waterjet cutting technology, is derived. In the framework of interpretation of measured values, relations among these parameters are systematically analysed and physico-mechanical and distributional principles governing these parameter are formulated newly. The generalization of these principles is done by means of analytically, correlationally, regressionally and empirically derived equations with a graphical representation of distribution of their functions...