Plot/Story
Imagine yourself in this scenario: It's the last day of 9th grade. You're going on a big school field trip that you've been looking forward to for months. You rush onto the bus in excitement and can't wait for a weekend of just hanging out with your buddies, eating smores over a hot campfire. Everything starts off awesome. You and your friends are laughing and having a good time on the bus, and you're about to confess to the chick you've liked since kindergarten. But suddenly you start to feel drowsy and eventually pass out. You wake up in a classroom with a collar around your neck. You teacher explains to your class that you'll all be released onto an island and forced to kill each other with no way to escape. And just to prove it ain't a joke, he throws a knife through some poor girl's head who was already more scared shitless than even you. Scary shit, huh?

And that is the great thing about the plot of Battle Royale. It draws you into a world that is truly horrifying, in which people your age (or younger) are forced to do away with all of their friends. Sure, the plot may not be very logical, but that's not the point. It's supposed to make you feel like you're really in that situation. It's supposed to make you scared for these kids, and at the same time question your own morality by making you think "What would I do in this situation?" Sure, the plot loses some originality points by being an adaptation, but most people who are reading this probably haven't read the book or seen the movie. But even if you have, it's still fun to see it portrayed in a different way. All in all, it's a great plot, that's sure to make you think. Oh, and I didn't include the details of why the kids are there because that's really not the point of the manga. It doesn't need some fancy explanation, because it focuses much more on that[/b[ the kids are there, not [b]why.
Characters
Shuya Nanahara: A good-hearted, innocent kid that only wants to rock out to an illegal genre of music, instead of having fun with all the girls throwing themselves at him like most boys his age would. He's a nice, sweet, innocent, noble kid that always wants to do the right thing. He seems a bit too light to be in a manga like this, and sometimes he's downright annoying. But thank god those instances are rare and that he's saved by the amazing supporting cast.

Noriko Nakagawa: The quiet, petite, shy, cute love interest. She doesn't really do much except provide motivation for the main character and add some sweet spots to the manga. Again, she's kind of out of place, but she's saved by the supporting cast. Her and Shuya almost seem like they belong in a Shounen manga, honestly.....

Shogo Kawada: A tough guy, whose intentions aren't quite clear and who seems to have a few dark secrets (mostly indicated by the bullet and knife scars all over his body). He's a very strong character, and arguably the most developed of all of them.

Kazuo Kiriyama: The main antagonist. Imagine a 15-year old Jason Voorhees with a fully-automatic instead of a machete. He's a sociopathic killer that doesn't express a hint of emotion except for one point in the story. He's a great antagonist, and the fact that he's completely sociopathic adds a bit of menace to him. He was probably my favorite character, but you'll most likely dissagree.

Mitsuko Souma: The 2nd antagonist. She's a cold-blooded killer similar to Kiriyama, but she expresses a much greater degree of emotion. She's that character that seems evil and heartless at first, but as the story goes on you start to see that there may be something we're not seeing. That there may be some good in her hidden deep beneath her great amounts of sadness, anger, hatred, and insanity.

Hiroki Sugimura: The martial-arts expert that always arrives at the right time to save everyone. He's a bit similar to Shuya, but he's much more likeable. He's very noble, but he doesn't show that naive "lets save everyone" shounen attitude that Shuya displays. He realizes full well that he's in the middle of a warzone.

Shinji Mimura: The jock with a heart. I'm sure everyone has met someone like him. Craved by every girl in the school, the star athlete, but still manages to have this incredible likeability. He's the kinda guy that you hate at first cuz you think he's just another asshole jock, but once you really start to talk to him you learn that he's willing to be friends with anybody, and look out for his buddies no matter what it takes. It's incredibly developed, but I'm not gonna get into any of that, because I intend for this review to not have any spoiler tags. Overall, he's one of my favorite characters, but at times he seems just a little bit to calm and understanding of his situation.

There are many other minor characters that I'm not going to get into, but they're all just as interesting as the main 6 or 7. Most are very developed and aren't just there to fill space. Overall, the characters in this manga are amazing. This is much more of a character-driven story than a plot driven story.
Drawing Style
I've noticed most people either love this art style or they hate it. There's no real in between. Personally I loved it and I can't see why anyone else doesn't. The attention to detail on everything from the characters to the weapons to the scenery to the gory deaths is just breathtaking. I'll admit, it definately isn't a normal style. It's kind of a weird cross between gritty realism and classic manga art. I know it sounds very goofy, but it's executed extremely well. Overall the art is just beautiful, but it's likely you'll disagree with me so please don't start arguing.
Enjoyment
This is one of the most enjoyable mangas I've ever read. Everything about it from the art to the characters to the plot just sucks you right in and never lets you go until the end. It definately doesn't seem like a 15 volume manga. The chapters go by incredibly quick and it's over so fast that I kinda wished it hadn't ended quite yet. This is one of those ones that just sucks you in.
Overall
This is probably as close to perfect as a manga can be. Everything is done almost flawlessly. It's definately a must-read for anyone remotely interested.