  This paper is concerned with the initial-boundary value problem \; for
stochastic transport equations in bounded domains. For a given stochastic
perturbation of the drift vector field, we prove existence and uniqueness of
weak solutions with non-regular coefficients. The existence of weak solutions
relies strongly on the existence of strong stochastic trace, and also on the
passage from the Stratonovich into It\^o's formulation for bounded
domains.Moreover, the uniqueness of weak solutions is obtained under suitable
conditions.
