The paper studies the system of a rigid body interacting dynamically with point vortices in a perfect fluid. For arbitrary value of vortex
strengths and circulation around the cylinder the system is shown to be Hamiltonian (the corresponding Poisson bracket structure is rather complicated).
We also reduced the number of degrees of freedom of the system by two using
the reduction by symmetry technique and performed a thorough qualitative
analysis of the integrable system of a cylinder interacting with one vortex.