Dive into a comprehensive lecture on quantum simulation presented by Nathan Wiebe from the University of Toronto at IPAM's Winter School on Contemporary Quantum Algorithms and Applications. Explore the origins and relevance of quantum simulation, delving into key concepts such as the Schrödinger equation, time evolution operators, and Hamiltonian simulation. Gain insights into compilation techniques and learn about Taylor's theorem and its proof as applied to quantum systems. Understand the strategic approaches used in quantum simulation and their potential applications in various fields of science and technology.