Weakly interacting Fermi gas is a generally accepted working model for description of electrons in metals. However, already 80 years ago E.Wigner predicted that at sufficiently low densities the Coulomb repulsion should be enough to crystalize even the gas consisting of only electrons. The problem with experimental observation of this crystal phase, e.g. in two dimensional semiconductor hetero-structures, is that it becomes melted by quantum fluctuations for the electron density exceeding some very low critical value. On the other hand, the electron\'s motion (fluctuations) in two dimensional systems is usually affected by the spin-orbit interaction, which become more and more important just at the low carriers density. In this talk, after a brief introduction into Wigner crystals, I will discuss, how the strong spin-orbit interaction of a Rashba form modifies drastically the properties of the crystalline phase. In the presence of spin-orbit the free electron spectrum splits into two subbands with the lower one having a Mexican hat shape with degenerate multiple minima. Individual electrons in a ground state of the crystal now should each pick up a particular momentum at the bottom of the subband, thus breaking not only the translational invariance in the coordinate space, but also the rotational invariance in the momentum plane. This leads to a number of interesting effects, including distortion of the original triangular lattice, formation of a lattice with two electrons per unit cell, non-trivial spin structures etc.

Colloquium, May 30th, 2013