The current theory of cosmic inflation is largely based on classical physics. This undermines its predictivity in a world that is fundamentally quantum mechanical. With this project we will develop a novel approach towards a quantum theory of inflation. We will do this by introducing holographic techniques in cosmology. The notion of holography is the most profound conceptual breakthrough that has emerged form fundamental high-energy physics in recent years. It postulates that (quantum) gravitational systems such as the universe as a whole have a precise `holographic’ description in terms of quantum field theories defined on their boundary. Our aim is to develop a holographic framework for quantum cosmology. We will then apply this to three areas of theoretical cosmology where a quantum approach is of critical importance. First, we will put forward a holographic description of inflation that clarifies its microphysical origin and is rigorously predictive. Using this we will derive the distinct observational signatures of novel, truly holographic models of the early universe where inflation has no description in terms of classical cosmic evolution. Second, we will apply holographic cosmology to improve our understanding of eternal inflation. This is a phase deep into inflation where quantum effects dominate the evolution and affect the universe’s global structure. Finally we will work towards generalizing our holographic models of the primordial universe to include the radiation, matter and vacuum eras. The resulting unification of cosmic history in terms of a single holographic boundary theory may lead to intriguing predictions of correlations between early and late time observables, tying together the universe’s origin with its ultimate fate. Our project has the potential to revolutionize our perspective on cosmology and to further deepen the fruitful interaction between cosmology and high-energy physics.