Dr. Smirnovas updated text is devoted to the theoretical studies of radiation effects on mammals. It summarizes 35 years of results the author obtained from analyzing dose rate equivalents for the Galactic Cosmic Rays (GCR) and for Solar Particles Events (SPE). This edition also includes two new chapters on skin epidermal epithelium and risk assessment for myeloid leukemia, as well as extended revisions addressing the radiation effects on the blood-forming system. Mathematical models are used to explain the effects of both acute and chronic irradiation on the dynamics of vital body systems, like the hematopoietic system, the development of autoimmune diseases, and the mortality dynamics in homogeneous and nonhomogeneous mammalian populations. The proposed methodology of these studies, the models themselves, and the obtained results are of a great theoretical significance and can find wide practical use.