  The paper is concerned with a system of linear hyperbolic differential
equations on a network coupled through general transmission conditions of
Kirchhoff's type at the nodes. We discuss the reduction of such a problem to a
system of 1-dimensional hyperbolic problems for the associated Riemann
invariants and provide a semigroup theoretic proof of its well-posedness. A
number of examples showing the relation of our results with recent research is
also provided.
