P-adic numbers play a very important role in modern number theory, algebraic geometry and representation theory. Lately P-adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the non-archimedean geometry of space-time at small distances. This is the first book to deal with applications of P-adic numbers in theoretical and mathematical physics. It gives an elementary and thoroughly written introduction to P-adic numbers and P-adic analysis with great numbers of examples as well as applications of P-adic numbers in classical mechanics, dynamical systems, quantum mechanics, statistical physics, quantum field theory and string theory.