In this paper we shall compute the cyclic cohomology of a non-commutative torus, i.e., a certain algebra associated with an antisymmetric bicharacter of a finite rank free abelian group G. The main result is 1.1 where The method of computation generalises the computation of the cyclic cohomology of the irrational rotation algebras given by Connes in [3]. (Our method works equally well also in the rational case, which was dealt with by a different method by Connes in [3].) We first describe the Hochschild cohomology of in an explicit way, and then combine this description with the exact sequence of [3]: 1.2
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