Topics in Quantum Chemistry -- Relativistic Quantum Theory of Many-Electron Systems -- Spurious Modes in Dirac Calculations and how to avoid them -- Tensor product approximation (DMRG) and Coupled Cluster Method in Quantum Chemistry -- Quantum Cluster Equilibrium -- Linear Response Methods in Quantum Chemistry -- Topics in Density Functional Theory and Related Approaches -- Progress on New Approaches to Old Ideas: Orbital-free Density Functionals -- Time-dependent Density Functional Theory -- Density Functional Theory for Strongly-Interacting Electrons -- Towards the Computational Design of Compounds from First Principles -- Application of (Kohn-Sham) Density Functional Theory to Real Materials -- The Quantum Energy agrees with the Muller Energy up to the Third Order -- Mathematical Aspects of Density Functionals and Density Matrix Functionals in Quantum Chemistry -- Some (important?) unsolved Mathematical Problems in Molecular Simulation -- Topics in Computer Science -- The Computational Complexity of Density Functional Theory -- Computational Techniques for Density Functional-based Molecular Dynamics Calculations in Plane-Wave and Localized Basis Sets -- Information Theory in Many-Electron Descriptions -- Towards the Information-Theoretic Construction of an Orbital-free Kinetic Energy Functional -- Lieb-Robinson Bounds and Simulation of Time Evolution of Local Observables in Lattice Systems -- Green Function-based Approaches -- Electronic Structure Calculations with LDA+DMFT -- The GW Approximation for the Electronic Self-Energy -- Topics in Quantum Monte Carlo and Related Approaches -- Levy-Lieb Principle meets Quantum Monte Carlo -- The new Resonating Valence Bond Method for ab-initio Electronic Simulations. Mathematical Perspective on Quantum Monte Carlo Methods -- Open Problems: A wish list of Mel Levy and Elliot Lieb.