  This mini-course provides a presentation of the method of characteristics to
initial/boundary-value problems for systems of first-order partial differential
equations and to Hamilton-Jacobi variational inequalities. In particular, these
results are indeed useful for the treatment of hybrid systems of control
theory.
  We rely on tools forged by set-valued analysis and viability theory, which
happen to be both efficient and versatile to cover many problems. They find
here unexpected relevance.
