Six chambers, Chambers 13 to 18, have Advanced variants that you can play after completing the normal game. The general layout of the advanced chamber is the same as the normal one, but a number of subtle and not-so-subtle differences make it considerably more difficult to play. For example, a floor that you placed portals on during the game may be non-portalable or even covered with toxic goo.
Walkthroughs of the advanced chamber variants are included in the individual Chamber pages. There, you can study them in the context of the normal chamber solutions. The links below take you directly to the advanced chamber sections of those pages: