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This book summarizes the author's work establishing a method to evaluate the gamma and electron radiation damage in terms of atom displacements. The proposed Monte Carlo assisted Classical Method relates the established theories about atom displacements to the electron and positron fluence distributions calculated from the Monte Carlo simulation. The proposal mainly consists in replacing the analytical distributions of particles produced in gamma and electron interactions with material by those obtained through the Monte Carlo simulation of radiation transport in matter. Full comparisons between the proposed method and previous theoretical estimations are presented and discussed. The book details the calculation of the displacements per atom distributions in some technologically relevant materials and devices, like the YBa2Cu3O7 superconductor ceramic and radiation detectors for medical applications based on lutetium-yttrium oxyorthosilicate and lutetium-yttrium orthoaluminate scintillators and cadmium zinc telluride semiconductor.