Chapter 1 Relativistic Quantum Theory of Many-Electron Systems

Chapter 2 Spurious Modes in Dirac Calculations and How to Avoid Them

Chapter 3 Tensor Product Approximation (DMRG) and Coupled Cluster Method in Quantum Chemistry

Chapter 4 Quantum Cluster Equilibrium

Chapter 5 Linear Response Methods in Quantum Chemistry

Chapter 6 Progress on New Approaches to Old Ideas: Orbital-Free Density Functionals

Chapter 7 Time-Dependent Density Functional Theory

Chapter 8 Density Functional Theory for Strongly-Interacting Electrons

Chapter 9 Towards the Computational Design of Compounds from First Principles

Chapter 10 Application of (Kohn–Sham) Density-Functional Theory to Real Materials

Chapter 11 The Quantum Energy Agrees with the Müller Energy up to Third Order

Chapter 12 Mathematical Aspects of Density Functionals and Density Matrix Functionals in Quantum Chemistry

Chapter 13 Some (Important?) Unsolved Mathematical Problems in Molecular Simulation

Chapter 14 The Computational Complexity of Density Functional Theory

Chapter 15 Computational Techniques for Density Functional Based Molecular Dynamics Calculations in Plane-Wave and Localized Basis Sets

Chapter 16 Towards the Information-Theoretic Construction of an Orbital-Free Kinetic-Energy Functional

Chapter 17 Lieb-Robinson Bounds and the Simulation of Time-Evolution of Local Observables in Lattice Systems

Chapter 18 Electronic Structure Calculations with LDA $$+$$ DMFT

Chapter 19 The GW Approximation for the Electronic Self-Energy

Chapter 20 Levy-Lieb Principle meets Quantum Monte Carlo

Chapter 21 The New Resonating Valence Bond Method for Ab-Initio Electronic Simulations

Chapter 22 Mathematical Perspective on Quantum Monte Carlo Methods

Chapter 23 On Some Open Problems in Many-Electron Theory