The angular momenta and parities of the low lying states of ¹³²Sn have been firmly determined through studies of the β-decay of ¹³²In. The lowest lying state with a negative parity is shown to have a collective octupole character. Several particle-hole multiplets have been identified, including the lowest lying proton excitation. Theoretical estimates of multiplet positions and multiplet splittings, based on the analogy with ²⁰⁸Pb, agree well with the data. More than about 20% of the theoretically estimated bound states of ¹³²Sn have been identified.