Despite being far from having reached 'artificial general intelligence' - the broad and deep capability for a machine to comprehend our surroundings - progress has been made in the last few years towards a more specialised AI: the ability to effectively address well-defined, specific goals in a given environment, which is the kind of task-oriented intelligence that is part of many human jobs. Much of this progress has been enabled by deep reinforcement learning (DRL), one of the most promising and fast-growing areas within machine learning. In DRL, an autonomous decision maker - the "agent" - learns how to make optimal decisions that will eventually lead to reaching a final goal. DRL holds the promise of enabling autonomous systems to learn large repertoires of collaborative and adaptive behavioural skills without human intervention, with application in a range of settings from simple games to industrial process automation to modelling human learning and cognition. Many real-world applications are characterised by the interplay of multiple decision-makers that operate in the same shared-resources environment and need to accomplish goals cooperatively. For instance, some of the most advanced industrial multi-agent systems in the world today are assembly lines and warehouse management systems. Whether the agents are robots, autonomous vehicles or clinical decision-makers, there is a strong desire for and increasing commercial interest in these systems: they are attractive because they can operate on their own in the world, alongside humans, under realistic constraints (e.g. guided by only partial information and with limited communication bandwidth). This research programme will extend the DRL methodology to systems comprising of many interacting agents that must cooperatively achieve a common goal: multi-agent DRL, or MADRL.