I've read about the universe expanding or contracting and about what shape the universe has. If the universe is a finite size, then what's outside the universe?
Science only seeks to answer certain questions. What exists "outside" the universe? What existed before the Big Bang? These are questions that scientists currently are not seeking. That question is left up to the philosophers for now.
The questions really point to a better understand of the universe and whether that question is important, relevant or even consistent with our present knowledge of the universe.
Astronomers and physicists find the surface of an expanding balloon a good analogy for the nature of our universe. The surface, just surface mind you, of that balloon has no center or edge to it. Just like how we understand the universe. The surface material of the balloon would be what we call space-time.
What is outside the surface of the balloon?
Well there is no balloon material outside so it is not space as we know it but one perspective says it is a future balloon surface. Just like inside the balloon was once a past balloon surface.
The universe could have a similar analogy.