Evaluating Feynman Integrals through differential equations and series expansions

We review the method of the differential equations for the evaluation of multi-loop Feynman integrals. In particular, we focus on the series expansion approach for solving the system of differential equation and we discuss how to perform the analytical continuation of the result to entire (complex) phase-space. This approach allow us to consider arbitrary internal complex masses. This review is based on a lecture given by the author at the “Advanced School and Workshop on Multiloop Scattering Amplitudes” held in NISER, Bhubaneswar (India) in January 2024.