1. Introduction

2. Completions of groups, Lie algebras and algebras

3. Monoidal categories and monoidal functors

4. Operads

6. Infinitesimal braids, $GRT_{1}$ and associators

7. Grothendieck-Teichmüller group, graph complexes and T.Willwacher theorems

8. Some applications of the theory of Drinfeld's associators, $GRT_{1}$ and graph complexes