Sahih Muslim is a collection of sayings and deeds of Prophet Muhammad (SAW), also known as the sunnah. The reports of the Prophet’s sayings and deeds are called ahadith. Imam Muslim was a student of Imam Bukhari. He lived a couple of centuries after the Prophet’s death and worked extremely hard to collect his ahadith. Each report in his collection was checked for compatibility with the Qur’an, and the veracity of the chain of reporters had to be painstakingly established.
Imam Muslim’s collection is recognized by the overwhelming majority of the muslim world to be one of the most authentic collections of the Sunnah of the Prophet (SAW).
It is important to realize, however, that this collection is not complete: there are other scholars who worked as Imam Muslim did and collected other authentic reports.