What are the specialized books in comparative Usul al-Fiqh, and those that extensively study comparative Fiqh for more than the four schools of thought (such as the Zahiri, Awza'i, and Bukhari)?

The important books on comparative Fiqh are: Al-Mughni by Ibn Qudamah, Al-Majmu' by Al-Nawawi, Al-Istidhkar by Ibn Abd al-Barr, and Al-Muhalla by Ibn Hazm. These books are considered rich sources for issues of disagreement among the early scholars (Salaf), and scholars have praised them for their importance and comprehensiveness.

As for books on comparative Usul al-Fiqh, they have been classified according to different methodologies: the Hanafis' method, the majority's method, a combination of both, deriving minor issues from major principles, and presenting principles through the lens of objectives (Maqasid). Among the most important books that combine the Hanafi and the majority methods are: Badi' al-Nizam by Al-Sa'ati, Tanqih Usul al-Fiqh by Sadr al-Shari'ah, Jam' al-Jawami' by Taj al-Din al-Subki, Al-Tahrir by Ibn al-Humam, and Muslim al-Thubut by Ibn Abd al-Shakur al-Hanafi, in addition to Al-Muhadhdhab fi Ilm Usul al-Fiqh al-Muqaran by Dr. Abd al-Karim al-Namlah.