If you've been a PC gamer for awhile, it's hard to imagine you don't already have some experience with Portal but, if you don't, I highly recommend you play it first as the Portal 2 story is a continuation of this. You will miss much of the humor and enjoyment of the dialogue by not being familiar with the history.
This game begins xxxxx years later with the same human character, Chell, awakening from stasis in the Aperture Science Enrichment Center. With GLaDOS presumably dead, the place has fallen into ruin and continues to disintegrate around your head. GLaDOS is the artificial intelligence computer system that Chell "killed" in the first Portal. Your first goal is to reach safety and to this end a new AI character to the series named Wheatley comes to your aid. The British actor Stephen Merchant received worldwide acclaim for this role and no wonder as he steals the show for humor. Those Brits sure know how to deliver a line.
When I first fired up Portal 2, I expected more of the infamous Portal chambers and indeed it's not long before you're once more at the mercy of the re-activated and vengeful GLaDOS. While she rebuilds Aperture, she also re-institutes the testing program and takes further revenge on Chell by mentally torturing her at every opportunity. GLaDOS' sarcasm knows no bounds as she continually reminds Chell that her parents abandoned her and intersperses these references with comments about Chell being fat. Of course, GLaDOS is plenty ticked off about being "murdered."
However, there is much more to Portal 2 than its chambers. Although the Portal games are puzzle oriented, what's great about this game is that your character is also given purpose for progressing through them. That purpose is the hope of escape and moving towards a specific goal is fully exploited in this sequel. Chell is imbued with a heightened sense of determined purpose that was more low key for most of the first game. In Portal, the game took a surprising turn near the end, but that happens much sooner in Portal 2. What we are left with in the middle portion is a hybrid between Portal and Half-Life minus the weapons. It's still puzzle driven, but it has a distinct Half-Life feel about it. For one thing, there is more story and character development and more history about Aperture and its origins. It's also about reaching destinations and how best to accomplish that. I don't know if any of the other reviews have commented on this similarity to Half-Life, but to me it was obvious.
In single-player, as I've mentioned, Wheatley the AI provides comic relief as well as scouting out ways to help you escape and defeat GLaDOS again. It's determined that Chell needs to make a core transfer between GLaDOS and Wheatley, but once accomplished, Wheatley turns to the dark-side. Intoxicated by the power, he too becomes obsessed with testing Chell. GLaDOS, however, has managed to just barely survive by plugging herself into a potato-operated battery. Now she allies herself with Chell to defeat Wheatley. It's ridiculously funny while also being darkly humorous in places where the AI preys on Chell's emotional weaknesses. But a revelation is waiting for GLaDOS as well, giving this tale much more depth. The story is all delivered through various devices as Chell remains completely quiet in both voice and thought. We are left to surmise her mind through her actions and the comments of the other characters.
The main tool is still the portal gun, which allows you to open up inter-spatial portals between two flat planes. It can only be used on specific surfaces, though, and finding these often requires ingenuity. New aids, in addition to the portal cubes that act as weights, have also been added in the form of laser beams, light bridges and various colors of gel with specific properties. These can also travel through a portal, so they add a great variety to puzzle solving and an element of just pure fun. Who can resist goo! It was a brilliant idea.
As to the actual puzzles, in my opinion, they are somewhat easier than in Portal, although there were a couple that had me scratching my head for awhile. However, for the most part the chamber puzzles follow a more structured line. It's fairly easy to ascertain what you have to do in order to move on and then just accomplish each step through to its conclusion. The puzzles outside of the chambers offer a little more challenge in determining your route. It's not overly easy to die, but you can do it by falling into any of the many toxic pools or by missing a jump from a dizzying height. In which case, you will re-spawn from a recent checkpoint.
The two-player co-op gives you entirely different characters. The robotic Atlas and P-Body each have a portal gun and are required to work together to solve test chambers.
Typical of Valve, they have enabled users to mod the heck out of this game with fan made downloadable chambers available in the thousands. There is a dedicated website and Steam workshop just for this purpose. Check under Mod Tools for the link.UPDATE Nov 2015: It's not often that Steam promotes fan-made mods in their store, but occasionally you see one pop up. Portal Stories: Mel is a free mod you can download from Steam if you own Portal 2. The huge mod was four years in the making and has a very positive rating. It will give you 6-10 hours of gameplay and is more of a complete game than a mod.