Real-world applications, such as queueing systems, communication networks and financial markets, evolve in a random fashion over time. Research in applied probability provides insight into these processes that exhibit randomness using results from the theory of probability, so that they can be mathematically modelled and better understood. These processes can model real world systems that evolve in a random fashion over time, for example:, queuing systems, communication networks and financial markets. Advances in stochastic approximation, non-Markovian random walks, stochastic control and such techniques have led to developments in other topics, including Monte Carlo Computation and Optimisation under Uncertainty. See also the Centre for Doctoral Training in Communications, which is one of our Interdisciplinary PhD programmes.