The Mikheyev-Smirnov-Wolfenstein (MSW) Effect

Developments of main notions and concepts behind the MSW effect (1978 - 1985) are described. They include (i) neutrino refraction, matter potential, and evolution equation in matter, (ii) mixing in matter, resonance and level crossing; (iii) adiabaticity condition and adiabatic propagation in matter with varying density. They are in the basis of the resonance enhancement of oscillations in matter with constant (nearly constant) density, and the adiabatic flavor conversion in matter with slowly changing density. The former is realized in matter of the Earth and can be used to establish neutrino mass hierarchy. The latter provides solution to the solar neutrino problem and play the key role in transformations of the supernova neutrinos.