This book presents the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics in a pedagogical, way and is mainly add

"...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.

This long awaited book is devoted to the methods of microlocal semiclassical analysis in application to spectral asymptotics with accurate remainder estimates.

This book corresponds to a graduate course given many times by the authors, and should prove to be useful to mathematicians and theoretical physicists.