Black hole and cosmological horizons -- from which nothing can escape according to classical gravity -- play a crucial role in physics. They are central to our understanding of the origin of structure in the universe, but also lead to fascinating and persistent theoretical puzzles. They have become accessible observationally to a remarkable degree, albeit indirectly. These lectures will start by introducing horizons and how they arise in classical gravity (Einstein's general relativity). In the early universe, the uncertainty principle of quantum mechanics in the presence of a horizon introduced by accelerated expansion (inflation) leads to a beautifully simple, and empirically tested, theory of the origin of structure. Its effects reach us in tiny fluctuations in the background radiation we observe from the time when atoms first formed.
This theory, and the observations, are sensitive to very high energy physics, including effects expected from a quantum theory of gravity such as string theory. Modeling the early universe within that framework helps us better understand the inflationary process and its observational signatures. Analyzing the `big data' from the early universe -- which continues to pour in -- is a major effort. This provides concrete tests of theoretical models of degrees of freedom and interactions happening almost 14 billion years ago.
Our understanding breaks down if we push further back in time, or into black hole horizons. This challenges us to determine more precisely how and why our existing theories fail. I will explain these basic puzzles, and conclude with some of the latest results on this question in string theory, which exhibits interesting new effects near black hole horizons.