The Gatsby Unit PhD programme was the first to combine theoretical neuroscience and machine learning within the same programme. Our mathematical approach for developing novel algorithms and tools to understand learning, perception and action in brain and machines is unique. Applications to this programme must be submitted directly to the Gatsby Unit via its online portal. The Gatsby Unit is a world-class research centre for Computational and Theoretical Neuroscience and Machine Learning. Our research seeks to understand the principles of learning, perception and action in brains and machines by developing mathematical algorithms. We provide a unique opportunity for a critical mass of theoreticians to interact closely with each other and with other UCL research groups, in particular the Sainsbury Wellcome Centre for Neural Circuits and Behaviour (SWC) as well as the Centre for Computational Statistics and Machine Learning (CSML). Teaching is supplemented with regular research talks, journal clubs and reading groups, external seminar series and participation in relevant conferences and workshops. PhD students will be supported by all academic staff, not just their immediate supervisors.