Automated computational analysis schemes for Western classical music analysis based on form and hierarchical structure have not received much attention in the literature so far. One reason, of course, is the paucity of labeled datasets — which, if available, could be used to train machine learning approaches. Dataset curation cannot be crowdsourced; one needs trained musicians to devote sizable effort to carry out such annotations. Further, such an analysis is not simple for beginners; obtaining labeled data that can capture the nuances of a musician's reasoning acquired over years of practice is fraught with challenges. To this end, we provide a system for computational analysis of classical music, both for machine learning and music researchers. First, we introduce a labeled dataset containing 200 classical music pieces annotated by form and phrases. Then, by leveraging this dataset, we show that deep learning-based methods can be used to learn Form Classification as well as Phrase Analysis and Classification, for which few (if any) results have been reported yet. Taken together, we provide the community with a unique dataset as well as a toolkit needed to analyze classical music structure, which can be used or extended to drive applications in both commercial and educational settings.