All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Many topics of the science of Mustalah Al-Hadeeth (Hadeeth terminology) are among the general topics dealt with in the books of Usool Al-Fiqh (principles of Fiqh). They are two sciences which overlap on several topics; therefore, you find the books of Usool al-Fiqh discussing the classifications of the Hadeeth in terms of Tawaatur (collectively contagious reports), Aahaad (a Hadeeth that is not Mutawaatir [i.e. any stage of its chain of narrators has less than ten narrators]), Saheeh (sound), Mursal (a Hadeeth narrated by a Tabi'i [successor of the Prophet's Companions]), Munqati‘ (a Hadeeth that has a discontinuous chain of narrators [e.g., a second generation narrator is missing before the name of the Companion]), and Mu‘dhal (a Hadeeth that has two or more narrators missing from its chain consecutively), and they also include the wordings of narrations, trustworthiness of narrators, the ways in which the narration is confirmed authentic, and other topics of Hadeeth which are mentioned in the Usool Al-Fiqh literature.
On the other hand, there are differences of opinion among the scholars, like those of the Shaafi‘i and Hanafi Schools, concerning some topics of Hadeeth, among which is whether a narration from an unknown person is accepted; the Shaafi‘i School and the majority of the scholars do not accept it, while the Hanafi School accepts it as long as the narrator is not known to be of bad moral character.
They also differ in opinion with regard to the Mursal Hadeeth; Abu Haneefah, Maalik and other Imaams are of the view that it is permissible to use it as evidence whereas the Shaafi‘i School and the majority of the scholars are not of the view that it is permissible to use it as evidence. The Shaafi‘i School said it may be used as evidence on condition that it is narrated by senior Taabi‘is (from the generation that followed the generation of the Companions), like the Mursal Ahaadeeth transmitted by Sa‘eed ibn Al-Musayyib. There are also other topics which you may review by referring to the books of Mustalah Al-Hadeeth.
Allaah Knows best.