With the help of syncretiсs as a new philosophical logic, the philosophy of carriers, the theory of similarity and the theory of Infinite Hierarchical Nesting of Matter, the problems of modern physics are analyzed. We consider the classical and relativistic mechanics, the special and general theories of relativity, the theory of electromagnetic and gravitational fields, of weak and strong interactions. The goal is axiomatization of these theories, building models of elementary particles and of their interactions with each other. The main obtained results are: the model of bead lightning; an explanation of redshift of the spectra of galaxies; the derivation of the Newton law in the concept of gravitons; the calculation of nuclear forces and the structure of simplest nuclei with the help of the theory of strong gravitation; building the model of weak interactions of elementary particles; presentation of quarks as a particular type of quasiparticles; explanation of the electron spin. The book should be useful for students and researchers, as well as for those interested in physical and philosophical problems.