It is the prudent thing to do for academic scholarship. That's not really a legal question. Whether using the information might constitute copyright infringement would require additional facts.
The above is general legal and business analysis. It is not "legal advise" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
If you're using other people's theories, or quotes, or unique research, then it's important (but not legally required) that you give them proper attribution in your material. Your material can build on what others have provided, but your material should not claim ownership of or origination of those unique elements that others have created.
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This is not a legal requirement but it is a good practice. The legal problem that you face is whether your use of information from other sources could violate copyright law. If your book copies substantial portions of someone else's writing on a given subject you could be accused of plagiarism. While copyright does not cover ideas and facts, it does cover original recitations of ideas and facts in tangible mediums of expression. If your book borrows too heavily from the words and paragraphs written elsewhere, you could be deemed to engage in copyright infringement. This is true even if your book combines writings from many different sources. It is ok to conduct research for facts, but when you write about the facts you must use your own words. Even when you try to do so, you can be accused of infringement if your description of the facts is substantially similar to the way the facts were presented in the sources that you used.
Anyone who writes books needs to educate herself on the basics of intellectual property law. A simple google search will reveal dozens of excellent web-sites that provide free, useful educational materials concerning copyright, trademark, and other IP laws.
In the broadest sense, the answer is "No." You can write a book, even a textbook, and not include a bibliography. However, if you are talking about some sort of textbook or reference guide, it is customary to recognize sources -- e.g., if you are writing a book about physics and refer to Newton's original notebooks, you would reference it to give credit where credit is due. That said, you don't have to refer to everything you looked at -- e.g., you don't need to cite Wikipedia or an NY Times article, etcetera, unless you are quoting from them.
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