The main goal is to introduce this subject to a wider audience in a more intuitive way. The course should ideally end with applications of derived algebraic geometry to constructing virtual fundamental classes in enumerative geometry using perverse sheaves.

Classical algebraic geometry, taught in graduate-level courses, is only a shadow of the complete framework offered by derived algebraic geometry. I will describe the new insights and applications that are offered by the latter while avoiding being as technical as the standard literature cited below.