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In the book, readers are offered the basics of the theory of processing blanks by abrasive tools, which are based on the probabilistic approach and systemic principles of analysis. A number of provisions of this theory are also formulated by Professor A. Korolev. The principles of analysis, modeling, design and management are considered. The operation is considered as a dynamic system, the state of which may vary during the period of processing the surface. The interaction between tool and work piece are treated as non-stationary stochastic process. The models for tracking the removal of material in the area of contact of the work piece with the tool, the wear of the abrasive tool, and the formation of the micro relief of the treated surface are proposed. Examples are given of the calculation of the current size, shape, surface roughness. The problems of using dynamic models for the synthesis of grinding processes are considered. Practical recommendations are given to improve thequality and efficiency of finishing and fine grinding processes.