Is there a book for the samfunnskunnskapsprøven?

There is no official book you need to buy. What exists is a curriculum and course material, and both are public.

The curriculum is the answer key

The curriculum in social studies for adult immigrants is a regulation. It has 25 competence goals, and the exam questions are designed around them. If you want to know what might come up in the exam, this is what applies, not a book.

Training under the Integration Act is 75 hours split across three modules of 25 hours each, and follows the same curriculum.

The course material is free

The official course material is available online and costs nothing. It's translated into all the languages the exam is offered in, so you can read it in your own language.

Why a book still isn't enough

A book tells you what's true. It doesn't tell you what you don't know. That's the difference, and it's the whole reason people study for weeks and still fail: they read from page 1, and their gaps are on page 60.

Take a practice test first, find the gaps, and read in a targeted way. It's faster and it works better.