`Ilm al-Hadith (علم الحديث): The general science of hadith that covers its terminology, classification, and methodology.
Ilm al-Rijal (علم الرجال) or Ilm al-Jarh wa al-Ta`dil (علم الجرح و التعديل): The science of biographical evaluation. It studies the lives, integrity, and reliability of the narrators in a hadith chain.
Mustalah al-Hadith (مصطلح الحديث): The terminology of hadith. It deals with the terms used by hadith scholars to classify and evaluate hadith, such as sahih (authentic), da’if (weak), hasan (good), etc.
Asma’ al-Rijal (أسماء الرجال): The names of narrators. This is often a component of `Ilm al-Rijal, focusing on cataloging and detailing the narrators.
`Ilm al-Matn (علم المتن): The study of the text of the hadith. It looks into the content and evaluates it for consistency, accuracy, and potential errors.
Ilm al-Itibar (علم الاعتبار): The science of considering or disregarding certain chains or narrators in the classification of hadith.
`Ilm al-Gharib (علم الغريب): The science of studying uncommon or difficult words and terms in hadith.
`Ilm al-Takrij (علم التكريج): Identifying the sources of various hadiths and locating where they can be found in the primary hadith collections.
Fada’il al-Sahabah (فضائل الصحابة): This refers to the merits and virtues of the Companions. While not strictly a science of hadith, it often relies heavily on hadith literature.
`Ilm al-Tashih wa al-Tarikh (علم التصحيح و التاريخ): The science of correcting mistakes in hadith and determining the chronological order of events.
`Ilm al-Musalsal (علم المسلسل): The study of hadiths that have a specific pattern in their chains, whether in terms of content or the way they were narrated.