Information theory is a branch of science that studies, from a mathematical perspective, the processing, transmission, and storage of information. The classical theory has been established in 1948 by Claude Shannon and has later been extended to incorporate processes where information is represented by the state of quantum systems.A major limitation of the present theory of information is that various of its concepts and methods require, as an assumption, that the processes to be studied are iterated many times. For example, Shannon's well-known result that the Shannon entropy equals the data compression rate assumes a source that repeatedly emits data according to the same given distribution. In addition, such results are often only valid asymptotically as the number of iterations tends to infinity.While this limitation is normally acceptable when studying classical information-processing tasks such as channel coding (since communication channels are typically used repeatedly), it turns out to be a severe obstacle when analyzing new types of applications such as quantum cryptography. For instance, there is generally no sensible way to describe the attack strategy of an adversary against a quantum key distribution scheme as a recurrent process.The goal of this project is to overcome this limitation and develop a theory of (classical and quantum) information which is completely general. Among the potential applications are new types of cryptographic schemes providing device-independent security. That is, their security guarantees hold independently of the details (and imperfections) of the actual implementations.