Resonant Raman and nuclear magnetic resonance spectroscopies from single gallium arsenide quantum dots are demonstrated. The nuclei were probed through changes in the optical spectra of the quantum dot exciton arising from exciton-nuclear interactions. This approach allowed the application of optical spectroscopy with its extremely high sensitivity and selectivity. The experiments had a lateral spatial resolution of about 10 nanometers and probe a volume that was five orders of magnitude smaller than that of previous semiconductor nuclear spectroscopic studies.