Physical properties often boil down to the arrangement of electrons within a solid, which means that mapping the electronic structure is a powerful way of classifying and understanding a wide range of materials. By applying ultrashort laser pulses with 22 eV photon energy from a novel 500 kHz extreme-ultraviolet light source to chains of indium atoms on a silicon surface, we are able to produce a detailed map of electronic states not normally accessible to traditional methods for measuring the electronic structure. The same technique also enables us to track the energy flow within the material as the highly excited electrons exchange energy with each other and the crystal lattice. Charting such previously inaccessible states and their dynamics allows us to better test the limits of current theories for understanding and predicting physical phenomena, and may in future lead to new designer materials.