1. Introduction
1. The Electronic Structure Problem in Condensed Matter
1. Ground Electronic State Properties vs. Excitations
2. Limiting Behaviors of Electrons in solids
3. Extended band-like (weakly-correlated) vs.
4. Localized atomic-like (strongly-correlated) behavior
5. Examples: H, Na, Si, Cu, Ni, NiO, La2CuO4, Ce,Tb
6. The Greatest Challenges: Transitions and Crossovers
2. Theoretical Background
2. Independent Electron Approaches
1. Basic Theoretical Foundations
1. Density Functional Theory for the ground state
2. Examples of widely-used functionals: LDA, GGAs
3. Examples in atoms - solution of 1d equations and results
2. Electron Bands in Crystals
1. Bloch Theorem and solution in terms of plane waves
2. Pseudopotentials for accurate plane wave calculations
3. Local Orbital and Tight-binding methods
4. Linearized muffin tin approaches
5. Iterative methods: Plane wave and grids in real space
3.  Iterative Solutions and atomic motion
1. Car-Parrinello classical Molecular Dynamics for electrons and atoms
4. Examples of Results
1. Bands in selected materials
2. Total energies: stable crystal structures; phase transitions; phonons
3. Simulations of liquids, alloys, disordered magnets, amorphous materials, etc.
5. Further topics
1. Perturbation theory ("2n+1 theorem")
2. Linear scaling Order N methods
3. Functionals beyond LDA and GGAs
3. Many-Body Approaches (to be modified later in course)
1. Key theoretical constructs
1. Quasiparticles, Fermi Liquid Theory, Luttinger theorem
2. Prototype problems
1. Jellium, Hubbard model, Anderson/Kondo model, Mott Insulator
3. Ground State methods
1. Quantum Monte Carlo
4. Excited States
1. Greens function methods for Quasiparticles, Hedin’s "GW" approach
4. Strongly Correlated Prototype Problems
1. Impurity Problems
1. Anderson/Kondo Problem and Heavy Fermions
2. Mott Insulator Problem
1. Hubbard Models and "Hi-Tc" problems