Our goal is to accurately determine bound-to-bound transition wavelengths and energy levels of the low-lying open-shell configurations 4f^4^, 4f^3^ 5d, 4f^3^ 6s, and 4f^3^ 6p of doubly ionised neodymium (Nd III) through high-resolution spectroscopy and semi-empirical calculations. The emission spectra of neodymium (Nd, Z=60) were recorded using Penning and hollow cathode discharge lamps in the region 11 500-54000cm^-1^ (8695-1852{AA}) by Fourier transform spectroscopy at resolving powers up to 106. Wavenumber measurements were accurate to a few 10^-3^cm^-1^. Grating spectroscopy of Nd vacuum sliding sparks and stellar spectra were used to aid line and energy level identification. For the analysis, new Nd III atomic structure and transition probability calculations were carried out using the Cowan code parameterised by newly established levels. The classification of 432 transitions of Nd III from the Penning lamp spectra resulted in the determination of 144 energy levels of the 4f^4^, 4f^3^ 5d, 4f^3^ 6s, and 4f^3^ 6p configurations of Nd III, 105 of which were experimentally established for the first time. Of the 40 previously published Nd III levels, one was revised and 39 were confirmed. The results will not only benchmark and improve future semi-empirical atomic structure calculations of Nd III, but also enable more reliable astrophysical applications of Nd III, such as abundance analyses of kilonovae and chemically peculiar stars, and studies of pulsational wave propagation in these stars.