  In this paper, we consider homogeneous cosmological solutions in the context
of the Weyl geometrical scalar-tensor theory. Firstly, we exhibit an
anisotropic Kasner type solution taking advantage of some similarities between
this theory and the Brans-Dicke theory. Next, we consider an isotropic model
with a flat spatial section sourced by matter configurations described by a
perfect fluid. In this model, we obtain an analytical solution for the stiff
matter case. For other cases, we carry out a complete qualitative analysis
theory to investigate the general behaviour of the solutions, presenting some
possible scenarios. In this work, we do not consider the presence of the
cosmological constant nor do we take any potential of the scalar field into
account. Because of this, we do not find any solution describing the
acceleration of the universe.
