Nobody really does, IMO. You read it so you know what kinds of things are topics in the field, what the most important results are, and mostly to get a feeling for what people in the field focus on.

Then when someone mentions a term from the course, you know roughly what to expect and where to find details. Also, you know how big a bite you're taking. "Quantum Mechanics" might be several books. "Vector Calculus" maybe a few chapters. "De Morgan's laws" maybe a few pages.

It's just like any other math you do. Does anyone memorize all the trig relations, Laplace transforms, and geometric relations? Of course not. But you've seen at least one large example of every topic and you can reconstruct it from there.