Diffusion tensor magnetic resonance imaging (DT-MRI) is unique in providing information about both the structural integrity and the orientation of white matter fibers in vivo and, through "tractography", revealing the trajectories of white matter tracts. DT-MRI is therefore a promising technique for detecting differences in white matter architecture between different subject populations. However, while studies involving analyses of group averages of scalar quantities derived from DT-MRI data have been performed, as yet there have been no similar studies involving the whole tensor. Here we present the first step towards realizing such a study, i.e., the spatial normalization of whole tensor data sets. The approach is illustrated by spatial normalization of 10 DT-MRI data sets to a standard anatomical template. Both qualitative and quantitative approaches are described for assessing the results of spatial normalization. Techniques are then described for combining the spatially normalized data sets according to three definitions of average, i.e., the mean, median, and mode of a distribution of tensors. The current absence of, and hence need for, appropriate statistical tests for comparison of results derived from group-averaged DT-MRI data sets is then discussed. Finally, the feasibility of performing tractography on the group-averaged DT-MRI data set is investigated and the possibility and implications of generating a generic map of brain connectivity from a group of subjects is considered.