Has anyone read Buddhism without belief?

Is it any good?
And what type of things does it teach?

I recommend you read up on Mindfulness. That'll point you in the right direction.

I haven't read that book.

I've read Confessions of a Buddhist Atheist by the same author.

Frankly, the term Buddhism without beliefs is already missing the point. No belief is a belief by the time you're talking about it.

I also reject his categorization of many of the moral precepts concerning thought as "thought crimes" to be terribly ignorant. It is our thoughts that sow the seeds of our actions in many cases. So one should absolutely strive to avoid thoughts like "I want to kill this person" or "I hate this person" and the like. It's fine to feel the hate and let it pass but identifying with it is a mistake. It's simply an impersonal mental factor that will arise and pass away. Not feeding into stuff like that is key.

He also seems to be under the idea that religion is a just-so-story that can be invented any which way.

So all together, I'm not exactly impressed with the author or the level of understanding that he has about Buddhism.