For the first time in the domestic literature, the results of research on the use of r-adic analysis in theoretical and mathematical physics are presented .. An introduction is given to the theory of r-adic numbers and non-archimedic geometry, a large number of results are given on integral calculus, the theory of generalized functions and pseudodifferential operators over the field of r-adic numbers .. Elements of classical and quantum mechanics over the field of p-adic numbers are presented, including the spectral theory of a quantum p-adic harmonic oscillator. Applications of r-adic analysis to quantum field theory, string theory, quantum groups, the theory of random processes. are described. For mathematicians and theoretical physicists-students of senior courses, graduate students, teachers and researchers .