Tons of great answers in this thread, but as you can see from my username, The Expanse is my favorite piece of media of all time. Both the books and TV show are god tier IMO. The show is one of the rare examples where the majority of the book readers agree that the show is a top tier adaptation, as opposed to a lot of other shows based off great books that the book readers don't like due to major changes. There are definitely changes to make the show flow better, but I'd say the changes are very well done and I've gone through all the books and novellas twice, and watched the show about 8 times all the way through.

Both the books and TV show are top tier sci-fi. Any sci-fi fan owes it to themselves to give either or both a shot!

They follow quite closely, as the authors were also show runners.

Each season is not exactly one book: season 1 is 2/3 of book 1, season two goes from there to half of book 2, season 3 wraps books 2 and 3. Seasons 4 to 6 are one book each.

Season 3 condenses book 3 quite a lot so you should expect differences here. As is usual in adaptation, characters and plot points are merged/moved around at diverse moments. A huge change is made at the end of season 5 due to one actor being outed as a perv piece of crap.

Books 7 to 9 were not adapted.

In the end, both mediums are great experiences and you should definitely enjoy both.

To be more specific: The show feels like the book authors took the opportunity to revise, edit, and improve their own work. The books provide extra context to some situations, Caliban's War in particular. But it's fun to see the smart decisions they made in the TV show to consolidate some characters and tweak storylines.