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This monograph deals with the results of the authors' research on both the study of the transport equation (the linear Boltzmann equation) and its applications in X-ray tomography. The introduction contains an outline of the text and deals with certain aspects of the methodology. The first part of the volume is devoted to the investigation of known and new problems for the stationary transport equation of a general form. New problems are treated as problems of tomography. The second part deals with the monoenergetic transport equation. c transport equation.