  These are notes on derived algebraic geometry in the context of animated
rings. More precisely, we recall the proof of To\"en-Vaqui\'e that the derived
stack of perfect complexes is locally geometric in the language of
$\infty$-categories. Along the way, we recall the necessary notions in derived
commutative algebra and derived algebraic geometry. We also analyze the
deformation theory and quasi-coherent modules over derived stacks.
