Asking physicians to carefully segment lesions in thousands of medical images in order to obtain a sufficient amount of data to train supervised deep learning models is not always a viable solution, since physicians are usually very busy, dedicating most of their time to diagnose and treat patients. One of the viable alternatives to supervised learning is reformulating the target task, e.g. tumor segmentation, as an anomaly detection problem, where the training data comprises only healthy (normal) examples, while the test data comprises samples with and without lesions. In this project, we plan to harness our previous experience in building self-supervised multi-task learning frameworks for image and video anomaly detection, to research, develop and test novel self-supervised multi-task learning methods for medical image anomaly detection. Our project is divided into two major phases: (1) the study of various self-supervised learning tasks specifically adapted for anomaly detection in medical images, and (2) the study of various combinations of self-supervised tasks to obtain viable self-supervised multi-task learning frameworks. Despite the high potential of self-supervised multi-task learning, to our knowledge, there are no previous studies on self-supervised multi-task learning for anomaly detection in medical images.