  These notes recall central elements of the cone calculus. The focus lies on
conically degenerate differential operators and the Laplace-Beltrami operator
with respect to a conically degenerate metric as a prototypical example. The
topics include manifolds with conical singularities, the Mellin transform, cone
Sobolev spaces, and the notion of ellipticity in terms of the invertibility of
the principal pseudodifferential symbol and the principal Mellin symbol. The
notes end with a sketch the full cone calculus.
  Lecture notes for a 3 hour course during the summer school 'Modern Problems
in PDEs and Applications' at Ghent University, Belgium, August 23 - September
2, 2023.
