2D collision without Box2D or Linecasts?

Im working on a 2D game and now its time to implement collision I don’t want to use the built in physics system because it messes up my pixel perfect setup. I’ve been looking for some tutorials but all of them are using linecasts or raycasts and that dosen’t seem so efficient for the performance. How would I implement simple 2D collision with using for example Rects (Or if theres any better method)?

The most simple collision would be AABB (Axis Aligned Bounding Box) if you looked up collision in games you will get a wiki page on different types of collisions if you wanted to write your own browse thorugh and see what takes your intrest