What are down-to-earth (i.e without $\infty$-categories for example) introduction to DG-categories ? I am mostly interested by applications to algebraic geometry. I know basic of category theory, homological algebra, algebraic geometry and a reasonable amount of sheaf theory.
I actually don't know much abstract homotopy theory (for example I don't know model category or I am not very familiar with localisation of categories). And I am not very familiar with stacks. If this is needed please tell me.
The purpose would be to understand papers in geometric representation theory and enumerative geometry where these ideas are appearing a lot it seems.
Best Answer
The ICM address of Bernhard Keller (https://arxiv.org/abs/math/0601185) is a perfect introduction.