This chapter introduces the general concepts of pair correlation, and superconductivity as a strong non-adiabatic phenomenon. Phonon, electronic, and magnetic mechanisms play the major roles; each of them can serve as the origin of the superconducting state. Speaking of the phonon mechanism, it is essential that an explicit expression for Tc depend on the intensity of the electron–phonon interaction. In principle, the electron–phonon mechanism can provide high values of Tc, up to room temperature. Pioneering work by Little, who introduced the electronic mechanism, is described. The mechanism has been analysed for one-dimensional, two-dimensional, and three-dimensional systems. The plasmon mechanism can play a role for layered materials. The superconducting state can be provided by magnetic degrees of freedom. The band limit with spin fluctuations and the regime of strong electron correlations are described. The Hubbard Hamiltonian and the t − J model are the ingredients of the approach.