Accel World

In 2046, people can access a virtual network known as the Neurolinker via their cellphone terminals. A perpetual victim of bullying, middle school student Haruyuki spends his time absorbed in games in a corner of his local network. One day he is approached by the most famous girl in his school, Kuroyukihime (Black Snow Princess). She gives him a strange program called Brain Burst that has the power to "accelerate the world."