An introduction to derived (algebraic) geometry

These are notes from an introductory lecture course on derived geometry, given by the second author, mostly aimed at an audience with backgrounds in geometry and homological algebra. The focus is on derived algebraic geometry, mainly in characteristic 0, but we also see the tweaks which extend most of the content to analytic and differential settings. The main motivating applications given are in moduli theory, with practically applicable representability theorems.