  The MSW (Mikheyev-Smirnov-Wolfenstein) effect is the adiabatic or partially
adiabatic neutrino flavor conversion in medium with varying density. The main
notions related to the effect, its dynamics and physical picture are reviewed.
The large mixing MSW effect is realized inside the Sun providing the solution
of the solar neutrino problem. The small mixing MSW effect driven by the 1-3
mixing can be realized for the supernova (SN) neutrinos. Inside the collapsing
stars new elements of the MSW dynamics may show up: the non-oscillatory
transition, non-adiabatic conversion, time dependent adiabaticity violation
induced by shock waves. Effects of the resonance enhancement and the parametric
enhancement of oscillations can be realized for the atmospheric and accelerator
neutrinos in the Earth. Precise results for neutrino oscillations in the low
density medium with arbitrary density profile are presented and the attenuation
effect is described. The area of applications is the solar and SN neutrinos
inside the Earth, and the results are crucial for the neutrino oscillation
tomography.
