Leviathan Wakes (2011) and its sequel novels are written by James S.A. Corey, which is in fact a pen name for two authors: Ty Franck and Daniel Abraham. The series originated as a science fiction role playing game imagined and set up by Franck. Abraham became a player and was so impressed by the world- er, solar system- which Franck had created that he asked for permission to write a novel based on the game. The two men ended up collaborating on that novel and its succeeding ones, and now both write and produce on the Prime series. I read somewhere (can't remember where) that the sudden death of one of the characters in the first book occurred because a player had to leave the game, so they killed off his character. Which is kind of amusing.
Leviathan Wakes was my "at work" book so was read in small chunks during my lunch breaks, and I quite enjoyed it. The novel covers the occurrences of the first season and about half of the second season of the show. The Expanse sticks quite closely to the tone, characters, and plot of the book- not surprising since the same writers are involved in both. There are some places where it's obvious that some plot points have been tweaked for the show- for example, in the novel James Holden uses the protomolecule sample as a bargaining chip with Fred Johnson. In the show, he insists that the sample be destroyed- and thinks that it has been. Also, the show introduces us to Chrisjen Avasarala and all of the drama occurring on Earth; she- and it- aren't present in Leviathan Wakes, it's my understanding that she shows up in one of the subsequent books.
The novel fleshes out a lot of the rather complex relationships- political and otherwise- between Earth, Mars, and the Belt, giving us a fuller understanding of the tensions, mutual distrust and resentments that flare to outright acts of violence, and eventually war. I also felt that the book gave me a better knowledge of the character and motivations of ex-cop Joe Miller, as we get in his head- hearing his thoughts- and also get more of his back story (such as his failed marriage). Curiously, in the case of two of the other main characters -Amos and Alex- the show actually gives us more fleshed out characters for them, as opposed to the novel. Although, of course, this may be rectified in later books.
To sum up, Leviathan Wakes was an enjoyable read and good science fiction. I recommend reading it as well as watching The Expanse and- here's something I never say- I don't think it really matters if you read it before or after you watch the show. The two are so close in tone and content that one will not spoil the other for you.