Volker Blum Duke University This talk introduces the practical aspects of electronic structure theory: Numerical techniques to discretize the Kohn-Sham Equations for non-periodic and periodic systems. Topics covered include basis sets, the calculation of Hamilton matrix elements, electrostatics, the Kohn-Sham eigenvalue problem, relativity, and efficient parallel implementations. These numerical pieces are common to all electronic structure methods; the example featured in this talk are the FHI-aims [1] all-electron electronic structure code and (for the eigenvalue problem) the massively parallel ELPA eigensolver library [2], also used in the practical sessions later in the workshop. [1] Volker Blum, Ralf Gehrke, Felix Hanke, Paula Havu, Ville Havu, Xinguo Ren, Karsten Reuter, and Matthias Scheffler, Ab initio molecular simulations with numeric atom-centered orbitals. Computer Physics Communications 180, 2175-2196 (2009). http://aims.fhi-berlin.mpg.de [2] Andreas Marek, Volker Blum, Rainer Johanni, Ville Havu, Bruno Lang, Thomas Auckenthaler, Alexander Heinecke, Hans-Joachim Bungartz, and Hermann Lederer, The ELPA Library - Scalable Parallel Eigenvalue Solutions for Electronic Structure Theory and Computational Science. The Journal of Physics: Condensed Matter 26, 213201 (2014). http://elpa.rzg.mpg.de