Why study compressed baryonic matter, or more generally strongly interacting matter at high densities and temperatures? Most obviously, because it's an important piece of Nature. The whole universe, in the early moments of the big bang, was filled with the stuff. Today, highly compressed baryonic matter occurs in neutron stars and during crucial moments in the development of supernovae. Also, working to understand compressed baryonic matter gives us new perspectives on ordinary baryonic matter, i.e. the matter in atomic nuclei. But perhaps the best answer is a variation on the one George Mallory gave, when asked why he sought to scale Mount Everest: Because, as a prominent feature in the landscape of physics, it's there. Compressed baryonic matter is a material we can produce in novel, challenging experiments that probe new extremes of temperature and density. On the theoretical side, it is a mathematically well-defined domain with a wealth of novel, challenging problems, as well as wide-ranging connections. Its challenges have already inspired a lot of very clever work, and revealed some wonderful surprises, as documented in this volume.