Kazumi Amano is the best student of the school; every girl talks to her with reverence, as Kazumi is definitely a step forward than others. Her abilities nevertheless do not derive form her natural talent but from her continuous diligence and devotion to work and training.   Kazumi Amano was already a senior at the Okinawa High School for Girls when Coach Ota selected her as a pilot candidate for the Gunbuster. She had previously demonstrated that she had marvelous potential after volunteering to participate in the Machine Weapon Junior Training Program in 2015.  The hard work she put into honing her skills allowed her to claim the title of Rose Queen, a title reserved only for the top female pilots in Japan. And Kazumi was the best at what she did, as she demonstrated during numerous class training sessions. During one of these training sessions is where she met Noriko Takaya.  Kazumi was shocked when she heard Noriko would be selected as her operating partner for the Gunbuster. She felt that Noriko should gain more experience, that picking a class freshman who could barely keep her RX-7 Trainer on its feet for actual combat duties was a fatal mistake. Coach Ota refused to listen to her and ordered Kazumi to continue working on her own skills. This only fueled Kazumi's passions, for she also secretly harbored love for him. This later played out to some certain extent by the heated arguments the pair had when Kazumi confronted him.  Kazumi married Ota in 2033 when she returned from the mission in which the Exelion was used to defeat the alien armada beyond Earth's solar system. She then remained behind on Earth as the new head coach for the Girl's School, picking up where her husband left off. In 2048 Kazumi accepted a promotion to colonel and returned to the Space Force to pilot Earth's massive new weapon against the aliens: the Black Hole Bomb.

In the very near future, a race of huge, insect like aliens is discovered traveling the galaxy. These aliens seem dedicated to the eradication of the human species as it takes its first steps away from the solar system, and they are getting closer and closer to Earth. Humanity has responded by developing spacegoing battleships and giant fighting robots. These robots are piloted by the best and brightest of Earth's youth, picked from training schools around the world. 
The story begins in the year 2023, not long after the first battles with the aliens, and centers on young Noriko Takaya. Although Noriko's father was a famous Captain in the space fleet who was killed during one of the first battles of the war, her own talents as a pilot are questionable. Nonetheless, she has entered a training school. Through the series Noriko, joined by the beautiful and talented Kazumi Amano, will fight to overcome the trauma of war, the doubts of her peers, and her own lack of confidence. 
(Source: AniDB)

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Extra science lessons included with the Gunbuster Blu-ray Box Complete Edition. These explain how the space ropeway works, and time dilation from near-lightspeed travel.

The science lessons are short "omake" bonus features originally present on the first two volumes. Each short lasts around two minutes, and stars super deformed versions of Noriko, Kazumi and the Coach explaining the various scientific aspects of the series. 
(Source: Wikipedia)

2 extra omake Science Lesson specials released on the LD-BOX set. Includes: Chapter 4+1 and Final Chapter.

This double feature comprises of Gunbuster and Die Buster (aka Gunbuster 2) condensed them into a single theatrical release told in two parts with a musical intermission in between. The first part, Gunbuster the Movie, condenses the six episodes of the original OVA into a 95-minute moviefeaturing a new 5.1 audio remix and a redub by the original Japanese cast. The second part, Die Buster the Movie, mixes large chunks of the second OVA series with a few altered or newly-animated scenes to create a truncated take on Nono's story. 
(Source: Anime News Network)

Comic Gunbuster is a compilation of short stories involving the main characters from "Aim for the Top" which take place during the time of the first OVA. Some of the stories include Kazumi Amano's marriage to Coach Ota and Noriko and Jung playing golf on the Moon. 
(Source: Anime News Network)