What is meant by "al-athar," and are there any books that discuss this branch, and what are the names of these books?

The word "athar" (tradition) is used for what has been narrated from the Prophet, peace and blessings be upon him, or from the Companions, regarding the Sunnah. Some scholars restrict its use to what has been narrated only from the Companions.

Some scholars differentiate between hadith and athar. Hadith and khabar (report) refer to what is narrated from the Prophet, peace and blessings be upon him, while athar refers to what is narrated from the Companions.

Among the books that dealt with the sciences of hadith are: "Al-Hadith al-Nabawi: Mustalahuhu, Balaghatuhu, Kutubuhu" (The Prophetic Hadith: Its Terminology, Eloquence, and Books) by Muhammad al-Sabbagh, and "Usul al-Hadith: Ulumuhu, wa Mustalahuhu" (Foundations of Hadith: Its Sciences and Terminology) by Muhammad al-Khatib. Among the books of the earlier scholars are: "Alfiyyat al-Iraqi," "Alfiyyat al-Suyuti," and "Muqaddimat Ibn al-Salah."