  We develop an operator formalism for investigating the properties of
nonabelian cosmic strings (and vortices) in quantum field theory. Operators are
constructed that introduce classical string sources and that create dynamical
string loops. The operator construction in lattice gauge theory is explicitly
described, and correlation functions are computed in the strong--coupling and
weak--coupling limits. These correlation functions are used to study the
long--range interactions of nonabelian strings, taking account of
charge--screening effects due to virtual particles. Among the phenomena
investigated are the Aharonov--Bohm interactions of strings with charged
particles, holonomy interactions between string loops, string entanglement, the
transfer of ``Cheshire charge'' to a string loop, and domain wall decay via
spontaneous string nucleation. We also analyze the Aharonov--Bohm interactions
of magnetic monopoles with electric flux tubes in a confining gauge theory. We
propose that the Aharonov--Bohm effect can be invoked to distinguish among
various phases of a nonabelian gauge theory coupled to matter.
