It is shown in this book that the weak electron-phonon interaction can play key role in single particle behaviour at proper conditions. It drastically changes properties of the system and cannot be treated by perturbation theory of any kind despite the small interaction constant: the weak interaction becomes a source of strong effects totally determining behaviour of a system. Contrary to the widely accepted opinion it results in self-trapping of a particle in the atomic size region in one-, two- and three-dimensional ideal crystals. In the case of resonance between an impurity electron transition and local or optical phonon mode weak electron-phonon coupling forms non-linear oscillation in which energy is reversibly transmitted between the impurity electron and the lattice in spite of the numerous lattice degrees of freedom. If the energy of an impurity electron transition exceeds considerably lattice frequencies and the electron is excited by powerful resonance laser wave, this interaction makes a resonance condition dependent on the lattice variables. Population of the upper electron level shifts an atom equilibrium positions and hence the energy of the electron transition; generated in this manner mismatch return the electron back and can result in self-trapping of the impurity electron at the ground state even for extremely strong pumping. Strong effects at weak electron-phonon coupling also take place if the lattice is in the vicinity of structure phase transitions. In this case, the lattice is very sensitive and even minor action results in strong response. This response is in the base of peculiar features of a sample in the region of phase transition. Strong and slow motion of the lattice forced by polaron hopping raises in critical region. Polaron driven lattice motion manifests itself in central peak (at zero frequency) in the neutron and light cross-section. All kinds of defects play crucial role in the vicinity of the phase transition. Lattice deformation produced by an impurity becomes large and long-range and may trap an electron (hole). Overlap of the deformations driven by different impurity results in long-distant (Coulomb-like) interaction between them. The author shows that surface of a crystal may be treated as a defect in the infinite crystal and also may trap carriers in the critical region. This planar defect may be at the nucleus where new phase raises before the phase transition in the bulk. In this case, the phase transition is two-step: at the surface at first and then in the bulk.