The jet space approach is a powerful tool to study invariant properties of PDEs, i.e. properties independent of the choice of coordinates (symmetries, conservation laws, recursion operators, etc.). The latest outcome of this approach is that, morally, the space of solutions of a PDE is a "derived manifold", which roughly means that vector fields, differential forms, etc. on it form "algebras up to homotopy". The aim of the talk is providing an introduction to the homological/homotopical algebra of PDEs.