what is derived algebraic geometry?

geometrical entities corresponding to dg-algebras

the space does not have points  , but it has a homotopy type

it is easier to understand what an Artin stack is in the context of derived geometry. The visitor was confused - 'how? I thought you know it?' The owner of the house said , 'It doesnt matter, it is the right thing to say'

The visitor said , ' but how? . . . ok nevermind, i'll think about it later . . but . . what is a koszul differential? '

the visitor , while he was leaving said, "  is Scholze's perfectoid space correct? "
The owner said , "yes it is completely correct .. a vector bundle is perfectoid '

'I'm a little scared of derived geometry the visitor said , while leaving '. The owner said, 'fine ,  just learn what an $A_\infty$ algebra is .. "
then there was a strange noise ,   and the light in the room  went out.