I was reading https://math.dartmouth.edu/~jvoight/notes/moduli-red-harvard.pdf, introduction of some notes on algebraic geometry (stacks, I do not know what it is) and came across following statement :
In beginning of algebraic geometry, one starts with varieties over the complex numbers, a set of points with a Zariski topology in which all points are closed points. In generalizing this to schemes, one asks for a locally ringed topological space equipped with a structure sheaf, allowing for closed and nonclosed points. To generalize this further, we define an object called a stack which will allow “points” equipped with nontrivial automorphisms: it will be a category with a Grothendieck topology.
I understand generalisation to schemes, spaces where we allow non closed points as well. But I do not understand what does it mean to say non trivial automorphisms and I am not at all aware of what a Grothendieck topology is.
Any information regarding that non trivial automorphism is welcome. I tried reading definition of Grothendieck topology but did not understand the definition.