\contentsline {section}{\numberline {1}Number Theory and $p$-adic Geometry}{3} \contentsline {section}{\numberline {2}Geometry in Characteristic $p$}{5} \contentsline {section}{\numberline {3}Coverings and Galois Theory}{6} \contentsline {section}{\numberline {4}A Perfectoid Point}{6} \contentsline {section}{\numberline {5}Perfectoid Spaces and the Tilt}{7} \contentsline {section}{\numberline {6}Examples of Applications}{7}