The notion of the Jacobian group of graph (also known as the Picard group, critical group, sandpile group, dollar group) was independently given by many authors (R. Cori and D. Rossin, M. Baker and S. Norine, N. L. Biggs, R. Bacher, P. de la Harpe and T. Nagnibeda an others). This is a very important algebraic invariant of a finite graph. In particular, the order of the Jacobian group coincides with the number of spanning trees for a graph. The latter number is known for many large families of graphs. But the structure of Jacobian in many cases are still unknown. The aim of the present lecture is  provide the structure theorems for Jacobians of circulant graphs.

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