The lectures give an introduction to on-shell methods for computing scattering amplitudes in quantum field theories. The first presents spinor variables and the construction of basic interactions without a Lagrangian. I will also give a derivation of the Britto-Cachazo-Feng-Witten on-shell recursion relations. The second lecture presents the framework for computing loop corrections to amplitudes. It describes the generalized unitarity approach, focusing on one-loop amplitudes. The third lecture focuses on Feynman integrals at higher loops. It will include an overview of the appliction of integration-by-parts to reducing integrals, and to deriving differential equations. I will also discuss recent advances in connecting integration by parts to aspects of the algebraic geometry of Feynman integrals.