Gunbuster OVA Series contains OVA episodes 1-6 of the anime directed by Hideaki Anno.

WANT TO AIM FOR THE TOP? ALL IT TAKES IS SOME HARD WORK AND GUTS!
THE ULTIMATE ANIME CLASSIC FINALLY COMES HOME IN HIGH-DEF!
FOR THE FIRST TIME ON BLU-RAY, WITH AN ALL-NEW ENGLISH DUB

When the space aliens killed Noriko Takaya’s father, she swore she’d go into space to have her revenge. Yet being accepted into the prestigious Okinawa Girls’ Space Pilot High School doesn’t solve every problem. Looked down upon as the daughter of the admiral who lost, and having a stark lack of talent that prevents her from piloting a machine, Noriko’s hopes for the future don’t seem bright. But then, when the two candidates going into space are announced, Noriko’s surprised to find her name right next to the star of the school (and Noriko’s own idol), Kazumi Amano. Has Noriko’s hard work paid off? Or is there more to Coach Ohta’s reasons for selecting her? Most of all, is Noriko really ready for the horrors of space? Find out in Aim for the Top!: Gunbuster, a true masterpiece of anime history, and Hideaki Anno’s directorial debut!