One of the curious things that the showrunners of The Expanse did was break things up somewhat by books, but not exactly. Season 3, however, contains the back half of the second book and the events of the third (a quick glance at Wikipedia tells me that quite a bit was changed from the novels).
Our crew has escaped Ganymede, and the Protomolecule hybrid. But Chrisjen is still in space aboard Mao's ship. Errinwright thinks he's free of Chrisjen, and is able to maneuver the UN Secretary General into war, but the Secretary General brings in an old colleague, Methodist Minister Anna Volovodov to help him write his speech for declaration of war.
The third season includes events on Io, the Mars/ Earth near all-out-war, as well as the evolution of the crashed Eros station on Venus as scientists try to sort it out - and the eventual escape of the structure built by the protomolecule, forming the ring on the edge of the solar system. They've also brought along a scientist from Ganymede, Prax, seeking his daughter who seems to have been kidnapped by her doctor.
The evidence of Errinwright's machinations makes it's way to the UN, ending the war.
With the Mars/ Earth war completed, and with peace a fragile thing, six months in, a convoy of Martian, Earth and Belter ships all head to The Ring - Earth sending civilians.
Of the many, many things The Expanse does well, it's very aware that not everyone in the future will be a rocket scientist, and we're going to still have our candidates for FailArmy out there (sorry, Star Trek) - a rocket-racing Belter deciding to be the first to race through The Ring on the promise of sex. And absolutely pancaking against an invisible wall of force.