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[en] The potential energy curves have been investigated for the 41 lowest doublet and quartet electronic states in the "2"s"+"1Λ"± representation below 55,000 cm"–"1 of the molecule BaF via CASSCF and MRCI (single and double excitations with Davidson correction) calculations. Twenty-five electronic states have been studied here theoretically for the first time. The crossing and avoided crossing of 20 doublet electronic states have been studied in the region 30,000–50,000 cm"−"1. The harmonic frequency ω_e, the internuclear distance R_e, the rotational constant B_e, the electronic energy with respect to the ground state T_e, and the permanent and transition dipole moments have been calculated in addition to static dipole polarizability of the ground state. By using the canonical functions approach, the eigenvalue E_v, the rotational constant B_v, and the abscissas of the turning points R_m_i_n and R_m_a_x have been calculated for the electronic states up to the vibrational level v=98. The comparison of these values with the theoretical results available in the literature shows a very good agreement. - Highlights: • We report 41 molecular states for the BaF molecule. • The spectroscopic constants have been calculated for the 41 low-lying states. • A ro-vibrational study have been performed up to the vibrational level v=98. • The permanent dipole moments have been investigated for 39 electronic states. • We present 25 new low-lying doublet and quartet excited states.