  The aim of this paper is to develop a Hamilton--Jacobi theory for contact
Hamiltonian systems. We find several forms for a suitable Hamilton-Jacobi
equation accordingly to the Hamiltonian and the evolution vector fields for a
given Hamiltonian function. We also analyze the corresponding formulation on
the symplectification of the contact Hamiltonian system, and establish the
relations between these two approaches. In the last section, some examples are
discussed.
