This project initiates a collaboration between high energy theorists and condensed matter theorists at Stanford, with the goal of advancing our understanding of theories of strongly correlated systems. The theorists involved will use promising new tools, including the holographic gauge/gravity duality, as well as more traditional effective field theoretic methods to obtain new solvable limits and qualitative insights into the nature of strongly correlated systems, especially non-Fermi liquid metals. Simultaneously, we will explore the emergence of spacetime itself in holographic theories, and its ties with the concept of entanglement in the dual quantum field theories. More concretely, projects to be undertaken include: new RG approaches to the study of quantum critical bosons interacting with a Fermi surface; Monte Carlo studies of lattice models of strongly correlated systems; classification of emergent horizons in gravity duals to strongly correlated systems, and characterization of transport and features of correlators (such as 2k_F singularities) therein; derivation of the Ryu-Takayanagi formula for holographic entanglement entropy; and direct field theory understanding of emergent dual holographic space-time geometries. There are close connections between the motivations, techniques, and ideas used in the various approaches, and we foresee many fruitful collaborations and new lines of inquiry emerging from this project. Ambitiously speaking, the outcome could be: improved holographic models of non-Fermi liquids that robustly capture experimental features of unconventional metals, and which work away from the limit of large N gauge theories; derivations of the dual spacetime descriptions directly from the path integral description of quantum field theories; and a better understanding of how quantum entanglement encodes and classifies strong correlations in novel states of matter.