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We give a survey of some results, mainly obtained by the authors and theircollaborators, on spectral properties of the magnetic Schr\"odinger operatorsin the semiclassical limit. We focus our discussion on asymptotic behavior ofthe individual eigenvalues for operators on closed manifolds and existence ofgaps in intervals close to the bottom of the spectrum of periodic operators.

Semiclassical analysis of Schr\"odinger operators with magnetic wells