Thanks to my boyfriend, we started watching Accel World some years ago and he suggested me to read the manga. He really liked it and thinks that the character of Kuroyukihime is more developed in the manga... I have to agree since in the anime you don't belive her and thinks that she will betray Haruyuki while in the manga you understand that she really loves him (and start to cheer for this ship XD).
The manga follows the anime for a lot of chapters but is faster and explains better the rules of Accel World and the relationships of the characters. We start with Haruyuki that is bullied and Kuroyukihime introduce him to a software called "Brain Burst" and the benefits that the software has (and even the side-effects). But that's not all: Kuroyukihime asks him to beat the game reaching the level 10.
The plot is easy but there's a lot of rules that are slowly explained and characters that have a lot of secrets. I really ike how the rules are explained and the characters develop. the drawings are especially well made and sometimes I stop to appreciate them.
A little note to say is that there are some chapters with a special guest in it (Kirito from Sword Art Online) and this is really interesting since for this special chapters the plot is quick, explain without telling too much plot of SAO and the battle Kirito VS Silver Crow is really exciting.
My rating: 10/10