Over the last term Jarod Alper has taught a course Introduction to stacks and moduli, introducing algebraic spaces and stacks and with the goal of proving (or outlining) properties of the stack $\mathcal M_g$ of curves, its compactification and their coarse moduli spaces. The recordings of the lectures are available and a pretty complete set of notes has been compiled.

The course only assumes prior familiarity with standard scheme theory, however a lot of other background material is covered in the appendices. One warning is that Jarod uses a bit of nonstandard terminology regarding stacks in general.