Nuclear magnetic resonance (NMR) is a powerful method for determining the structure of molecules and proteins(1). Whereas conventional NMR requires averaging over large ensembles, recent progress with single-spin quantum sensors(2-9) has created the prospect of magnetic imaging of individual molecules(10-13). As an initial step towards this goal, isolated nuclear spins and spin pairs have been mapped(14-21). However, large clusters of interacting spins-such as those found in molecules-result in highly complex spectra. Imaging these complex systems is challenging because it requires high spectral resolution and efficient spatial reconstruction with sub-angstrom precision. Here we realize such atomic-scale imaging using a single nitrogen vacancy centre as a quantum sensor, and demonstrate it on a model system of 27 coupled C-13 nuclear spins in diamond. We present a multidimensional spectroscopy method that isolates individual nuclear-nuclear spin interactions with high spectral resolution (less than 80 millihertz) and high accuracy (2 millihertz). We show that these interactions encode the composition and inter-connectivity of the cluster, and develop methods to extract the three-dimensional structure of the cluster with sub-angstrom resolution. Our results demonstrate a key capability towards magnetic imaging of individual molecules and other complex spin systems(9-13).