Numerical General Relativity is the art of solving Einstein’s Field Equations with computational methods. These lectures will review the formalism currently employed for astrophysical simulations in strong-gravity, notably comprising compact binaries, gravitational collapse and gravitational waves. They will cover the following topics: 3+1 formulation of Einstein’s equations, the initial data problem, the evolution problem, the gauge choice and the extraction of gauge-invariant quantities. A selection of breakthrough results for gravitational-wave astronomy will also be presented.