Microlocal analysis allows one to precisely describe the singularities of functions and distributions (generalized functions), and analyze how operators transform these singularities. The locations of singularities are expressed in terms of the cotangent bundle, which includes both spatial location and momentum (phase space) direction. Since many of the material parameters one is interested in medicine have discontinuities across interfaces, microlocal analysis lends itself to applications in medical imaging. This two-lecture mini-course will present some of the basics of microlocal analysis,

including a discussion of elliptic partial differential operators, their fundamental solutions and hypoellipticity; the notions of support, singular support and wave-front set; the calculus of pseudodifferential operators;and construction of parametrices for elliptic pseudodifferential operators.