  A (meromorphic) quadratic differential is a (meromorphic) section of the
tensor square of the canonical bundle of a Riemann surface. They arose in the
study of quasiconformal mappings in the works of Oswald Teichm\"uller, and have
played a mayor role in the study of the Riemann moduli, where they can be
identified with cotangent vectors to the moduli space. In more recent years,
inspired by several observations by Kontsevich, Soibelman and Seidel, in
arXiv:1302.7030 Bridgeland and Smith identified certain spaces of meromorphic
quadratic differentials with the space of stability conditions on a
triangulated category related to the underlying topological surface.
  This work is an attempt to give a complete (and as self-contained as
possible) account of the theory needed to define some families of quadratic
differentials (and a natural parametrization of such families). This families
are the basic building blocks used by Bridgeland and Smith in their study of
the spaces of quadratic differentials.
