Do I have to learn the truth tables if I already know how it works?

I already understand how “not”, “and”, and “or” works.

Can I just skip these pages and move on?

Or these are actually important for later on?

You really need to learn this. If there is something you need to learn really well and make cards of, it’s truth tables.

If you already have a background in math or something that taught you formal logic then it’s not necessary. I’d say go through the test that’s there and see how you do at figuring out the logic quizzes, and if you do well then move on. If you do poorly then memorizing the tables helps a lot.