In this thesis, we investigate different possibilities for artificial electron lattices. Electrons located on the surface of a copper crystal are trapped in a lattice due to the presence of carbon monoxide molecules on the surface, which act as a barrier to the 2D electrons. These molecules are placed using a scanning tunnelling microscope with atomistic precision. We first examine the Kekulé lattice. This lattice, formed by alternating strong and weak bonds in a honeycomb structure, allows us to introduce crystalline topology into artificial electronic systems. Next, we vary the amount of carbon monoxide molecules confining the electrons in the classical honeycomb lattice and find that it is possible to measure isolated p-orbital linear and flat bands. Muffin-tin simulations reveal that the effect of intrinsic spin-orbit coupling in these p-bands is relatively large, leading to more robust spin-orbit band gaps. This robustness is sought after for the realization of the quantum spin Hall effect. Finally, we predict that the coupling between both spin and (effective) angular momentum and a perpendicular magnetic field can be measured in both square and round quantum corrals.