  We study noncommutative vortex solutions that minimize the action functional
of the Abelian Higgs model in 2-dimensional noncommutative Euclidean space. We
first consider vortex solutions which are deformed from solutions defined on
commutative Euclidean space to the noncommutative one. We construct solutions
whose vortex numbers are unchanged under the noncommutative deformation.
Another class of noncommutative vortex solutions via a Fock space
representation is also studied.
