Tensor-Based Morphometry (TBM) allows the automatic mapping of brain changes across time building 3D deformation maps. This technique has been applied for tracking brain degeneration in Alzheimer's and other neurodegenerative diseases with high sensitivity and reliability. Here we applied TBM to quantify changes in brain structure after completing a challenging adaptive cognitive training program based on the n-back task. Twenty-six young women completed twenty-four training sessions across twelve weeks and they showed, on average, large cognitive improvements. High-resolution MRI scans were obtained before and after training. The computed longitudinal deformation maps were analyzed for answering three questions: (a) Are there differential brain structural changes in the training group as compared with a matched control group? (b) Are these changes related to performance differences in the training program? (c) Are standardized changes in a set of psychological factors (fluid and crystallized intelligence, working memory, and attention control) measured before and after training, related to structural changes in the brain? Results showed (a) greater structural changes for the training group in the temporal lobe, (b) a negative correlation between these changes and performance across training sessions (the greater the structural change, the lower the cognitive performance improvements), and (c) negligible effects regarding the psychological factors measured before and after training.