  Proving local well-posedness for quasilinear problems in pde's presents a
number of difficulties, some of which are universal and others of which are
more problem specific. While a common standard, going back to Hadamard, has
existed for a long time, there are by now both many variations and many
misconceptions in the subject.
  The aim of these notes is to collect a number of both classical and more
recent ideas in this direction, and to assemble them into a cohesive road map
that can be then adapted to the reader's problem of choice.
