By E. E. "Doc" Smith. These are generally thought to be his best work, and are the best known.
The anime movie using the title is so hacked that fans of the books are advised to avoid it.
Mild SPOILERS for the books are given in some of the discussion.
Five short stories and a longer piece (which was adapted into the Lensman universe). If you're doubtful about the Lensman books or Doc Smith, don't start here.
On the other hand, the WWII-era story is one of the best things I've ever read. Chemist goes to work in an explosives manufacturing plant during WWII, earns the respect of the technical people, and runs into wartime bsiness politics.
Another piece of backfill (Galactic Patrol was written and published first), but this one is a very good piece of backfill. This tells the story of Virgil Samms realizing the need for the lens, and being given it by the Arisians. And his trips to various other planets to try to recruit lensmen of other species. And it also contains the story of Rod Kinnison's run for President.
This is the official beginning of the series, and the debut of Kimball Kinnison. I started reading here myself. Nothing about the Eddorians, and little about the Arisians, is revealed in this book, though Kimball Kinnison does go to Arisia for advanced mental training.
At the end of the last book, Kinnison thought everything was pretty well cleaned up, but this turns out not to be the case; the problem is larger, wider, and deeper than he thought.
Kimball and Clarissa have finally had children, and in fact their son Kit has just graduated as a Lensman. Finally, a set of beings exist who can bring the conflict between Arisia and Eddore to a conclusion.
Also published as The Vortex BlasterNot a part of the Lensman series, but set in the Lensman universe. The scope is smaller, but the writing and characterization are classic Doc Smith, and there is perhaps a greater level of playfulness. How the mismatched set of individualists "Storm" Cloud assembles into his crew manage to work together is pretty enlightening.
There's also a lovely sequence on cheating at cards and roulette, and a good introduction to what "random" really means.
There's a very fine Lensman FAQ available.
I'm accumulating the references to "space gods", Klono and Noshabkeming, and related material, here.
I'm accumulating interesting vocabulary tidbits as I come across them here.