Additive Group Theory and Non-unique Factorizations.- Notation.- Basic concepts of non-unique factorizations.- The Davenport constant and first precise arithmetical results.- The structure of sets of lengths.- Addition theorems and direct zero-sum problems.- Inverse zero-sum problems and arithmetical consequences.- Sumsets and Structure.- Notation.- Cardinality inequalities.- Structure of sets with few sums.- Location and sumsets.- Density.- Measure and topology.- Exercises.- Thematic seminars.- A survey on additive and multiplicative decompositions of sumsets and of shifted sets.- On the detailed structure of sets with small additive property.- The isoperimetric method.- Additive structure of difference sets.- The polynomial method in additive combinatorics.- Problems in additive number theory, III.- Incidences and the spectra of graphs.- Multi-dimensional inverse additive problems.