  The Guillemin-Uribe trace formula is a semiclassical version of the Selberg
trace formula and more general Duistermaat-Guillemin formula for elliptic
operators on compact manifolds, which reflects the dynamics of magnetic
geodesic flows in terms of eigenvalues of a natural differential operator (the
magnetic Laplacian) associated with the magnetic field. In this paper, we give
a survey of basic notions and results related with the Guillemin-Uribe trace
formula and provide concrete examples of its computation for two-dimensional
constant curvature surfaces with constant magnetic fields and for the Katok
example.
