Descent And étale-Brauer Obstructions For 0-Cycles

This thesis is an expository article about the obstruction theory for 0cycles.Firstly,we introduce the obstruction theory in the context of rational points;then we introduce the Brauer-Manin set of 0-cycles and some relevant techniques;finally,the main part of the thesis is about the descent set of 0-cycles newly constructed by F.Balestrieri and J.Berg,and some applications they have given.