The sequel to Legend of the Galactic Heroes: Die Neue These Second.

The Free Planets Alliance's invasion of the Galactic Empire has failed after supply mismanagement led to heavy losses. Unwilling to abort the expedition despite being greatly outnumbered, Fleet Admiral Lazar Lobos orders the remaining Alliance fleets to gather in the Amritsar Starzone for a final stand against the incoming counterattack. 
 
Strategic genius Fleet Admiral Reinhard von Lohengramm leads the Imperial forces into this decisive battle with an overwhelming advantage. However, his rival, tactical magician Vice Admiral Yang Wen-li of the Alliance, once again makes up for the incompetence of his superiors and stages a narrow escape for himself and his fellow soldiers. Though both Reinhard and Yang are displeased with the outcome—the former for his imperfect victory and the latter for the tremendous casualties—their attention must turn to the bubbling political unrest on both sides of the galaxy. 
 
(Source: MAL Rewrite)

Faithful to novels, except some changes may be considered major, e.g., some characters changed from male to female.  Covers volume 1 and 2 of the novels.

For decades, the Galactic Empire has been locked in an interstellar war with the Free Planets Alliance, a conflict that involves thousands of spaceships and millions of soldiers on both sides. Two new commanders enter the conflict with great hopes: Imperial Admiral Reinhard von Lohengramm and the FPA's Yang Wen-Li. As they deal with superiors and subordinates, maneuver through complicated political arrangements, plot strategies, and win battles, each will be tested, and ultimately, changed, by the reality of war. 
(Source: Anime News Network)

The sequel to Legend of the Galactic Heroes: Die Neue These - Collision.
 
Note: It received a limited special screening in theaters with the episodes spliced together into 3 separate movies.

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