We study T-duality for open strings in various $D$-manifolds in the approach of canonical transformations. We show that this approach is particularly useful to study the mapping of the boundary conditions since it provides an explicit relation between initial and dual variables. We consider non-abelian duality transformations and show that under some restrictions the dual is a curved $(d-{\rm dim}G-1)$ D-brane, where $d$ is the dimension of the space-time and $G$ the non-abelian symmetry group. The generalization to $N=1$ supersymmetric sigma models with abelian and non-abelian isometries is also considered.

24 pags, latex file, some references added (version to be published in Nucl. Phys. B)