We present MapReader, a free, open-source software library written in Python for analyzing large map collections. MapReader allows users with little computer vision expertise to i) retrieve maps via web-servers; ii) preprocess and divide them into patches; iii) annotate patches; iv) train, fine-tune, and evaluate deep neural network models; and v) create structured data about map content. We demonstrate how MapReader enables historians to interpret a collection of ≈16K nineteenth-century maps of Britain (≈30.5M patches), foregrounding the challenge of translating visual markers into machine-readable data. We present a case study focusing on rail and buildings. We also show how the outputs from the MapReader pipeline can be linked to other, external datasets. We release ≈62K manually annotated patches used here for training and evaluating the models.