In a seminal work from 1975, B. Simon and E.H. Lieb put Hartree-Fock theory for non-relativistic atoms on a sound mathematical foundation. They proved the existence of a minimizer of the Hartree-Fock functional, and properties of the corresponding one-electron orbitals, e.g. regularity away from the nucleus, and exponential decay. In this project we plan to study the equivalent problem for so-called 'pseudorelativistic' atoms (the kinetic energy of the electrons is given by the squareroot of p2+m2).