These lecture notes on selected topics in numerical methods for hyperbolic equations are from renowned academics in both theoretical and applied fields, and include contributions on nonlinear hyperbolic conservation laws; first-order schemes for the Euler equations; high-order accuracy: monotonicity and non-linear methods; high-order schemes for multidimensional hyperbolic problems; and a numerical method for the simulation of turbulent mixing and its basis in mathematical theory. Lecture Notes on Numerical Methods for Hyperbolic Equations is intended primarily for research students and post-doctoral research fellows.