This course aims to give a comprehensive introduction to the theory of multiple zeta values and iterated integrals. It will cover not only basic topics but also advanced ones, including recent progresses of the theory.

We will discuss

• Overview of periods
• Hyperlogarithms and multiple zeta values
• Double shuffle relations
• Modular phenomena and the depth filtration
• Integral-Series identity of Schur multiple zeta values
• Special families of relations (Ohno's relation/Kawashima's relation etc.)
• Tangential basepoint and regularization of divergent iterated integrals
• KZ equation and Drinfeld associator
• Goncharov's coaction formula for hyperlogarithms
• Brown's theorem
• Goncharov's differential equation and confluence relations (basic case)
• Iterated beta integrals
• Finite multiple zeta values and Kaneko-Zagier conjecture
• q-analog

as long as time permits.