First, confirm that the open textbook you want to adapt has a license that allows modification and redistribution on the scale you need.
The most common open licenses are Creative Commons licenses. As long as the Creative Commons license does not have a “No Derivatives” (ND) clause, you’re free to change the contents of the book and redistribute with attribution. You don’t need to ask the author for permission. Speaking of permission, pay special attention to non-text materials such as illustrations, charts, diagrams, or items marked “used with permission,” as they may not be covered by the Creative Commons license.
If you’re unsure about the license or what to do about third-party content cited in the textbook or “used with permission,” contact someone who understands copyright law for advice. Your library, university counsel, scholarly communications office, or copyright officer are good places to begin.
People who share content with an open license may be receptive to inquiries about uses not covered by their selected license. It may be worth contacting the author or rights-holder with your questions.