What is the difference between the author and the verifier of a book? Is it a condition for all scholarly books to have an author and a verifier? What is the introduction (or foreword) that appears at the beginning of a book, and who writes it?

The author is the one who wrote and composed the book. As for the muhaqqiq (editor/verifier), he is the one who regularizes its text, compares its various copies, and corrects its errors. The term "tahqeeq" (editing/verification) emerged recently with the advent of printing. Every book has an author, but it does not necessarily have a muhaqqiq. Often, the biographies of authors found in the prefaces of books are the work of the muhaqqiq and the publishing house, and it is not known that an author in the Islamic heritage would write his own biography.