Okay, so the other reviewer has rightly pointed out that the premise of this particular manga is patently absurd. So, if you can't suspend your disbelief long enough to buy that a high school kid can encrypt code with a pencil and paper or that a virtual reality program could blow up the world, then you shouldn't be reading this manga. Please, go read something else.
For those of you who are left, you will find an enjoyable, short story. There is a nice little romance here and an absurd plot about AI. But the core of this manga, the reason to read it, are the themes: family, love, generosity and forgiveness.
The artwork is pretty good, but nothing to write home about. Everything is clean and clear, but I don't remember it sticking out as particularly wonderful either.
I will say that the manga was a lot more fun than it had any right to be, given the absurdity of the plot. Maybe because the plot was so silly, but I just found myself laughing the whole way through--sometimes at it, sometimes with it, but laughing nonetheless.
Is Summer Wars a great manga? Certainly not. But it's not bad either. If you are willing to take the absurd plot for what it is and just let yourself go along for the ride, it's an awful lot of fun.