  This text is the write-up of a series of lectures on the asymptotic mixed
Hodge theory of isolated hypersurface singularities, held at the Third Latin
American school on Algebraic Geometry and its applications (ELGA 3) in
Guanajuato, Mexico, in august 2017. Its focus is on the classical application
of the semi-continuity of the spectrum due to Varchenko and Steenbrink to the
problem of bounding the possible singularities on a projective hypersurface.
