There's a lot of content in this series. To reduce this review down to the bare essentials, I found it interesting to think and analysis all the political, subterfuge, military strategy/logistics, and philosophical concepts interwoven within the story and plot line.
All I had to do was to analyze the data the episodes gave me and extrapolate the logical conclusion and that would be the truth, because the world was made very consistent according to principles of history and human nature. This series is based upon a light novel so certain transitions and word flares were cut out to make room for the battles, the plots, the betrayals, the deaths, and the heroic empire building. This forced me to actually think about the world they were building and whether it made sense or not. Considering that the intellectual fortitude of the series required a lot of military (ground) strategy, logistical comprehension, political calculation, data/intel analysis, and a bunch of other stuff, there was more than enough material to stress the gray matter.
This series almost has everything. Love, battles, stories about empires lost and won, political fights won and lost, rebellions and revolutions, on top of betrayals and tragic deaths of heroic individuals. So much stuff is interesting and fun, that it was not hard to decide to give this series 5/5. It was one of the first series I rated the full rank here at Anime Planet. After watching another 50 anime series, my judgment hasn't changed even though I did some great amounts of reconsideration.
I surmise that the reason why there is a love and hate relationship for those that have seen or dropped Legend of Galactic Heroies is because LOGH requires the viewer to be educated in certain critical fields. It doesn't require you to be experienced in everything, such as battles, political analysis, or philosophical ethics, but unless you have a background in one subject at least, you'll be lost and unwilling to devote the time necessary to finish the series. The series requires a lot of viewer comprehension of certain key elements in military history, political corruption, and human nature for the viewer to be interested. Otherwise it's like reading scientific technical novels. You might as well read a plot summary.