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.• Footnotes tend to contain details and comments which are tangential to the main thread of the notes; they are excessive in number.• We adhere strictly to the standard convention that the indices in chain complexes and simplicial objects, and related operations and constructions, are denoted with subscripts, while those in cochain complexes and cosimplicial objects are denoted with superscripts; to do otherwise would invite chaos.• We intermittently write chain complexes V as V • to emphasise the structure, and similarly for cochain, simplicial and cosimplicial structures. The presence or absence of bullets in a given expression should not be regarded as significant.• We denote shifts of chain and cochain complexes by [n], and always follow the convention originally developed for cochains, so we have M [n] i := M n+i for cochain complexes, but M [n] i := M n−i for chain complexes.