  The general stationary cylindrically symmetric solution of Einstein-massless
scalar field system with a non-positive cosmological constant is presented. It
is shown that the general solution is characterized by four integration
constants. Two of these essential parameters have a local meaning and
characterize the gravitational field strength. The other two have a topological
origin, as they define an improper coordinate transformation that provides the
stationary solution from the static one. The Petrov scheme is considered to
explore the effects of the scalar field on the algebraic classification of the
solutions. In general, these spacetimes are of type I. However, the presence of
the scalar field allows us to find a non-vacuum type O solution and a wider
family of type D spacetimes, in comparison with the vacuum case. The mass and
angular momentum of the solution are computed using the Regge-Teitelboim method
in the case of a negative cosmological constant. In absence of a cosmological
constant, the curvature singularities in the vacuum solutions can be removed by
including a phantom scalar field, yielding non-trivial locally homogeneous
spacetimes. These spacetimes are of particular interest, as they have all their
curvature invariants constant.
