Abstract
These notes basically contain a material of two mini--courses which were read in Göteborg in April 2015 during the author visit of Chalmers & Göteborg 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.
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