I'm trying to learn how portal rendering engines work.

Reading old posts give me some idea about how they work but, I don't know how the more complicated things work.

There are no complete tutorials about how to make portal rendering engines and I want to go beyond the basics.

Where can I learn more about the math used and go deeper into how it works?

Are there any books that go into great detail on how to make a portal rendering engine?

Can you elaborate on your goals a little, and maybe on what sort of problems you're facing?

I'll admit I don't know that much about what leading engines are doing currently, but I think it's safe to say that conventional wisdom about and approaches to things like visibility and culling have changed significantly over time. A 'pure' portal system is, I think, a fairly specialized approach that's best suited for certain (perhaps somewhat limited) types of environments. Maybe I'm wrong though and it's of more general relevance than I think.

In any case, it might be easier to answer if you could tell us more about the context.