This course will cover the basics of quantum simulation, with a focus on cold-atom platforms. There will be two major directions: (i) Mapping quantum many-body models onto analog quantum-simulation platforms that are amenable for experimental realization, (ii) exploring the far-from-equilibrium properties of quantum many-body models. Crucial for both directions will be exact diagonalization methods, which will be a main focus of the course and the project component thereof. The course will have a research element to it, as we will be covering the latest in quantum simulation and far-from-equilibrium quantum many-body physics, and it will aim to bring the student up to speed on the state of the art in these fields. Quantum Mechanics I and II are prerequisites.