Recent years have seen the birth and growth of quantum machine learning, a new discipline which uses quantum computers for data analysis. Within this field, many heuristics have been proposed and to some extent individually tested. Yet, there is no truly holistic framework to study and characterize the essence and quality of all quantum machine learning models. Our plan is to provide rigorous statements to help building a solid fundament for a general theory of quantum machine learning. This can be done by applying results from statistical learning, Fourier analysis, quantum information, differential geometry, etc. to learning tasks in which the learner is assumed to have acces to a quantum hypothesis class. We hope to answer fundamental questions of trainability, expressivity, and generalization; as well as painting a unified picture for the future study of quantum machine learning models.