The Mainz Institute for Theoretical Physics will host a 2020 summer school for Ph.D. students in theoretical physics, the fifth of an annual series. The main theme of the school is "Scattering Amplitudes", ranging from recent new formal developments to precision calculations. Topics include lectures on the geometry of scattering amplitudes, on mathematical functions associated to loop amplitudes, on phenomenological applications in jet physics and on applications in perturbative gravity. The aim of the school is thus to provide a concise overview of the most important theory tools to carry out innovative research in the field of scattering amplitudes.