Theoretical and numerical details of an optimized LCAO (linear combination of atomic orbitals) method for the calculation of self-consistent bandstructures are given together with a variety of examples. The method will be a valuable tool both for researchers engaged in calculations and for scientists looking for numerical results of self-consistent bandstructure calculations. The presentation starts with an introduction to the modern many-body theory of electronic bandstructure. The essentials of the representation with a non-orthogonal basis and the usual tight-binding variants are...