Transformation optics grew out of ideas for invisibility cloaking devices and exploits connections between electromagnetism in media and in geometries. Invisibility has turned from fiction into science since 2006, but is far from being practical yet. Advances in the theory of transformation optical are the key for bringing invisibility closer to practicality. Probably the most important practical application of connections between media and geometries is perfect imaging, the ability to optically transfer images with a resolution not limited by the wavelength. This is because imaging lies at the heart of photolithography, the key technology used for making electronic chips. On the other hand, probably the intellectually most important application of connections between media and geometries lies in the quantum physics of the event horizon, which, for the first time, could be studied in the laboratory. The objective of this proposal is to make significant breakthroughs in (1) moving cloaking from frontier research closer to practicality, (2) turning perfect imaging into a viable technology and (3) demonstrating the quantum physics of the event horizon in the laboratory. This project is at the cutting edge of a global communal effort in the research of metamaterials. The overarching theme of the project is to make abstract and seemingly fantastic ideas practical, by combining ideas from geometry and general relativity with the latest advances in optical metamaterials and integrated and ultrafast photonics.