Theoretical background and computational methods.
Basic theory.
Density Functional Theory "DFT"(Walter Kohn, the 1998 Noble prize in Chemistry)
The best definition could be: "An exact theory ! ... and a practical method of applying quantum mechanics for many electron systems".
Inspired from Paul Dirac's view in 1929:
"The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It there fore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation."
Extensions.
Hybrid DFT (DFT + HF), mean-field like DFT+U, Time-Dependent DFT and DFPT
...and Beyond.
DFT+ Many Body techniques (GW and BSE...etc), for excitations and optical properties.
DFT+ DMFT (Dynamical Mean Field Theory), for strongly correlated systems.
Methodology. I'm mainly working with :
Augmented Spherical Wave (ASW) Method. One of the fastest codes for electronic structure calculations. Developed and maintained by Dr. Volker Eyert.
Projector Augmented Wave (PAW). A very accurate and efficient all-electron electronic structure method by Prof. Dr. Peter E. Blöchl. The original implementation i.e, CP-PAW code, for simulation of electronic structure and ab-initio molecular dynamics.
A good command on other codes and methods:
Linear Augmented Plane Wave (LAPW), all electron method. codes: Wien2k and Exciting
Quantum ESPRESSO (mainly: PW-scf). Suite of Open-Source computer codes for electronic-structure and materials modeling. Based on plane waves, and pseudo-potentials.