  We give a detailed proof of T. Willwacher's theorem arXiv:1009.1654 which
links the cohomology of the full graph complex fGC to the cohomology of the
deformation complex of the operad GER, governing Gerstenhaber algebras. We also
present various prerequisites required for understanding the material of
arXiv:1009.1654. In particular, we review operads, cooperads, and the cobar
construction. We give a detailed exposition of the convolution Lie algebra and
its properties. We prove a useful lifting property for maps from a dg operad
obtained via the cobar construction. We describe in detail Willwacher's
twisting construction, and then use it to work with various operads assembled
from graphs, in particular, the full graph complex and its subcomplexes. These
notes are loosely based on lectures given by the first author at the Graduate
and Postdoc Summer School at the Center for Mathematics at Notre Dame (May 31 -
June 4, 2011).
