This volume adapts what I'd describe as the "First Asuka Arc", with Asuka's arrival at Tokyo 3, and the "dance fight".
Asuka's characterization is slightly different from the anime, as she acts like much more like a bully problem child, putting on a goody-two-shoes air in front of the adults, but a much more abusive face when they're not looking. It makes for a different take on the character. Whether it's one for the better I'll have to see.
Also, all the problems with how Sadamoto draws the fights are completely gone in this volume. The dance fight is one that, in the wrong hands, could have failed horribly, but here it just works. That said, it also is lessened a little bit by the fact that we don't have the music, which would really help. That said, I mentally went with "Dance of the Hours" by Amilcare Ponchielli.