Abstract: We explore the electronic and the optical properties of monolayer TiS3, which shows in-plane anisotropy and is composed of a chain-like structure along one of the lattice directions. Together with its robust direct band gap, which changes very slightly with stacking order and with the thickness of the sample, the anisotropic physical properties of TiS3 make the material very attractive for various device applications. In this study, we present a detailed investigation on the effect of the crystal anisotropy on the excitons and the trions of the TiS3 monolayer. We use many-body perturbation theory to calculate the absorption spectrum of anisotropic TiS3 monolayer by solving the Bethe-Salpeter equation. In parallel, we implement and use a Wannier-Mott model for the excitons that takes into account the anisotropic effective masses and Coulomb screening, which are obtained from ab initio calculations. This model is then extended for the investigation of trion states of monolayer TiS3. Our calculations indicate that the absorption spectrum of monolayer TiS3 drastically depends on the polarization of the incoming light, which excites different excitons with distinct binding energies. In addition, the binding energies of positively and the negatively charged trions are observed to be distinct and they exhibit an anisotropic probability density distribution.