Usul Hadith is a science that relates to the study of hadith. It considers whether the chain and text of a single narration is authentic or not. This allows the scholars to only derive rulings and establish Aqaa’id based on rigorously authenticated hadith only.
One of the earliest known scholars who discussed the principle of hadith is Imām al-Tirmidhī. Imam Ibn al-Athir (a famous muhaddith) says in his Jami’ al-Usul, “Tirmidhī’s work is the finest, most beneficial, least repetitive and has the best arrangement. It also stands out by mentioning the different opinions and ijtihad [of the jurists], and clarifying the different types of hadith authentication, i.e. sahih, hasan, gharib. It also has some aspects of critical analysis of narrators.”
Other scholars of hadith would have also applied principle of hadith to authenticate individuals and hadith, but their methods have not been fully documented.
Around 200 years after Imam al Tirmidhi, al-Khatib al-Baghdadi (d. 463 AH) wrote Al-Kifayah fil `Ilm al-Riwayah. The first standalone, all-encompassing, well-organised textbook of Usul al-Hadith. He also wrote Al-Jami` li-Akhlaq al-Rawi wa Adab al-Sami`, a reference book on the etiquette’s of narration and Hadith recording. In addition, al-Khatib wrote numerous treatises covering every aspect of Hadith sciences.
Then another 200 years later, Ibn al-Salah (d. 643 AH) wrote ‘Ulum al-Hadith, also known as Muqaddimat Ibn al-Salah. This is a comprehensive text that is still studied in most Islamic institutions. There have been numerous abridgements and summaries, e.g. Imam al Nawawi’s Irshad Tullab al-Haqa’iq, Ibn Kathir’s Ikhtisar `Ulum al-Hadith, al-`Iraqi’s al-Taqyid wal-Idah, and Ibn Hajar’s Nukat. As well as poems, al-`Iraqi’s Alfiyah and al-Suyuti’s Alfiyah.
Then another 200 years later, Ibn Hajar Asqalani (d. 852AH) wrote Nukhbat al-Fikar fi Mustalah Ahl al-Athar. This was an attempt to canonise the rules and methodologies of Hadith scholars. It is a small work. Ibn Hajar supplemented the work with a commentary called Nuzhat al-Nazar Fi Tawdih Nukhbat al-Fikar.
Another couple of commentaries that are popular are Qafw al-Athar fi Safwat `Ulum al-Athar by Radiyy al-Din al-Halabi al-Hanafi and al-Far` al-Athith fi Usul al-Hadith to point out the differences between the Hanafis and Shafi`is.
Aside from this commentaries have only ever further expounded upon existing principles.
Alongside Usool Hadith, there have been books on Asma ar-Rijaal, the science of the condition, births, deaths, teachers and students of narrators. The most popular which are Tahdheeb al-Kaamil of Imaam Yoosuf Muzee, Tahdheeb at-Tahdheeb of Haafidh Ibn Hajr and Tadhkirratul-Huffaadh of ‘Allaamah Dhahabee.