  Over the last year significant progress was made in the understanding of the
computation of Feynman integrals using differential equations. These lectures
give a review of these developments, while not assuming any prior knowledge of
the subject. After an introduction to differential equations for Feynman
integrals, we point out how they can be simplified using algorithms available
in the mathematical literature. We discuss how this is related to a recent
conjecture for a canonical form of the equations. We also discuss a
complementary approach that allows based on properties of the space-time loop
integrands, and explain how the ideas of leading singularities and d-log
representations can be used to find an optimal basis for the differential
equations. Finally, as an application of the differential equations method we
show how single-scale integrals can be bootstrapped using the Drinfeld
associator of a differential equation.
