The application of boundary integral techniques to the study of mixing of viscous fluids is presented. Single Layer and Double Layer Representations for Stokes flows in bounded domains are formulated and numerical examples of mixing in selected geometrically-challenging two and three-dimensional problems are illustrated. Emphasis is given to the analysis of errors encountered in the point evaluation of the velocity field and the calculation of subsequent trajectories in time-perodic flows. It is shown that even though individual particle paths are sensitive to the accumulation of discretization errors, mixing templates can be calculated with reasonable accuracy. A simple error control formula is used that enables a systematic application of boundary integral methods to compute mixing patterns in time-periodic (chaotic) Stokes flows.