  In these lectures we discuss some of the mathematical structures that appear
when computing multi-loop Feynman integrals. We focus on a specific class of
special functions, the so-called multiple polylogarithms, and discuss introduce
their Hopf algebra structure. We show how these mathematical concepts are
useful in physics by illustrating on several examples how these algebraic
structures are useful to perform analytic computations of loop integrals, in
particular to derive functional equations among polylogarithms.
