The low-lying electronic states of Al-3 ((2)A(1),B-2(1),(4)A(2),B-4(1),B-2(2),(2)A(1),B-4(2),(6)A(2)) and Al-3(-) ((1)A(1),B-3(2),(3)A(1),(3)A(2),B-3(1),(5)A(2)) are studied by coupled-cluster methods with a [6s5p2d1f] basis set. The geometries and harmonic frequencies are calculated by the coupled-cluster single double triple (CCSD(T)) correlation method with frozen core and virtual molecular orbitals. The energetic splittings at CCSD(T) geometries are calculated also by the CCSDT method. The calculated vibrational frequencies of the observed states of Al-3 ((2)A(1), B-2(1), and (4)A(2)) and Al-3(-) ((1)A(1) and B-3(2)) are in excellent agreement with experimental results. Other frequencies of this work are expected to be correct within +/-20 cm(-1). It is shown that (4)A(2)-B-4(1)(E-4 ") and B-2(2)-(2)A(1)(E-2＇) Of Al-3 as well as B-3(2)-(3)A(1)(E-3＇) and (3)A(2)-B-3(1)(E-3 ") Of Al-3(-) are pairs of minima and transition states on a potential energy surface of a pseudorotation of the corresponding degenerate states. The vertical excitation energies of additional states of Al-3(2E＇,E-4＇,(2)A(1)＇) and Al-3(-)(E-1 ",E-1＇) are calculated by the electron-excitation equation-of-motion CC method and the electron-attachment equation-of-motion CC method. The possible processes of ionizations and vibronic transitions are analyzed based on the calculated results. All features of the recent photoelectron spectroscopic study of Al-3(-) are explained consistently. It is also shown that the photoelectron signals of electron binding energies of 2.65 and 4.4 eV in earlier experiments correspond to the ionization of the ground state of Al-3(-) to higher-lying excited states of Al-3. The two states of the resonant two-photon ionization experiment are assigned to the lowest quartet state and the third quartet state, E-4 "-->E-4＇, Without ambiguity. The anticipated features of five more electronic excitations with transition energies of 0.22, 0.69, 0.77, 0.98, and 1.06 eV are discussed.