Using an ab initio approach based on non empirical pseudopotentials for the Mg2+ and Li+ cores, Gaussian basis sets, effective core polarization potentials and full configuration interaction calculations, the adiabatic potential energy curves, the spectroscopic constants, the permanent and transition electric dipole moments of the several lowest electronic states of the alkali-alkaline earth ion MgLi+ have been performed. These states dissociate into Me(3s and 3p) + Li (2s, 2,p, 3s, 3p, 3d, 4s, 4-p, and 4d) and Mg (3s(2), 3s3p, 3s4s, 3s3d, 3s4p, 3s5s, and 3s4d) + Li+. The spectroscopic constants (Re, De, Te, omega(e), omega(e)x(e), and B-e) of the ground state and nearly 53 excited states of (1,3)Sigma(+), (1,3)Pi, and (1,3)Delta symmetries are derived. Most of them are computed for the first time. Moreover, several avoided crossings between the electronic states of (1,3)Sigma(+), (1,3)Pi symmetries are localized and analyzed. Their existence is related to the interaction between the potential energy curves and to the charge transfer process between the two ionic systems Mg+Li and MgLi+. Furthermore, accurate adiabatic permanent and transition dipole moments for several transitions have been calculated for a large and dense grid of internuclear distances for the first 15 (1)Sigma(+) electronic states. A linear behavior is observed in the permanent dipole moments for several electronic states. Additionally, the transition electric dipole moments between neighbor states have shown many peaks situated around the avoided, crossing positions.