The action in Grey Lensman picks up immediately where Galactic Patrol left off, in the middle of the battle to destroy Helmuth's Main Base and, it is hoped, fully end the threat of Boskone.
The clues lead Kinnison to mount an expedition aboard the newly constructed super-dreadnought Dauntless, into the Second Galaxy where he thinks the true head of Boskone might reside.
Kinnison decides that since the Patrol is not yet strong enough to attack the Second Galaxy militarily, he will follow leads to the upper levels of Boskone through the traffic in the illegal drug thionite.
The weapon they invent, whose theory requires the development of a wholly new mathematics, is called a "negasphere", composed of something combining the attributes of antimatter and negative matter.
Kinnison infiltrates Jalte's base and gets the information he had been hoping for since his trip to the Second Galaxy: the location of the leaders of Boskone, a group made up of members of a race called the Eich.
Infected by something that requires the Patrol doctors to amputate all four limbs, blinded, and tortured almost to death, Kinnison is nonetheless saved, but he will most likely be a basket case.
Earlier in the book, a Posenian physician called "Phillips" was financed by the Patrol to try to develop a way to allow higher beings to regenerate body parts in the same way that lower animals (starfish, flatworms, salamanders, etc.)
Groff Conklin gave the novel's first edition a scathing review in Galaxy, describing it as a "primitive artifact" which "simply gives [me] alternate waves of incredulous laughter and dull, acid boredom.