  These notes provide a description of the abelian categories that arise as
categories of coherent sheaves on weighted projective lines. Two different
approaches are presented: one is based on a list of axioms and the other yields
a description in terms of expansions of abelian categories.
  A weighted projective line is obtained from a projective line by inserting
finitely many weights. So we describe the category of coherent sheaves on a
projective line in some detail, and the insertion of weights amounts to adding
simple objects. We call this process `expansion' and treat it axiomatically.
Thus most of these notes are devoted to studying abelian categories, including
a brief discussion of tilting theory. We provide many details and have tried to
keep the exposition as self-contained as possible.
