  These notes basically contain a material of two mini--courses which were read
in G\"{o}teborg in April 2015 during the author visit of Chalmers &
G\"{o}teborg universities and in Beijing in November 2015 during
"Chinese--Russian Workshop on Exponential Sums and Sumsets". The article is a
short introduction to a new area of Additive Combinatorics which is connected
which so--called the higher sumsets as well as with the higher energies. We
hope the notes will be helpful for a reader who is interested in the field.
