  We present a complete list of 6-dimensional Manin triples or, equivalently,
of 3-dimensional Lie bialgebras. We start from the well known classification of
3-dimensional real Lie algebras and assume the canonical bilinear form on the
6-dimensional Drinfeld double. Then we solve the Jacobi identities for the dual
algebras. Finally we find mutually non-isomorphic Manin triples. The complete
list consists of 78 classes of Manin triples, or 44 Lie bialgebras if one
considers dual bialgebras equivalent.
