Ṣaḥīḥ Muslim is a collection of hadīth compiled by Imām Muslim ibn al-Hajjāj al-Naysāburi(rahimahullāh). His collection is considered to be one of the most authentic collections of the Sunnah of the Prophet (ﷺ), and along with Ṣaḥīḥ al-Bukhārī forms the "Sahihain," or the "Two Sahihs." It contains roughly 7500 hadīth (with repetitions) in 57 books.
The translation provided here is by Abdul Hamid Siddiqui.

Imām Muslim's full name is Abu al-Husayn Muslim ibn al-Hajjāj ibn Muslim ibn Warat al-Qushayri al- Naysaburi (206-261 AH/821-875 AD). Imām "Muslim," as his nasba shows, belonged to the Qushayr tribe of the Arabs, an offshoot of the great clan of Rabi'a.

He was born in Naysabur (Nishapur) in 206/821. His parents were righteous people who left such an indelible impression on his mind that he spent his life as a God-fearing person and always adhered to the path of righteousness. Imām Muslim travelled widely to collect hadith in Arabia, Egypt, Syria and Iraq, where he attended the lectures of some of the prominent Muhadith of his time: Isḥāq b. Rāḥawayh, Aḥmad b. Hanbal, 'Ubaydullah al-Qawariri, Qutaiba bin Sa’id, 'Abdullah ibn Maslama, Harmalah bin Yahya, and others. After completing his education, he settled down at Nishapur. There he came into contact with Imām al-Bukhārī. Imām Muslim was impressed with Imām al-Bukhārī's knowledge that he kept himself attached to him up to the end of his life. Another muhaddith that influenced Imam Muslim was Muhammad ibn Yahya al-Dhuhali and he attended his lectures regularly, but when the difference of opinion between Muhammad b. Yahya and Imam Bukhari on the issue of the creation of the Holy Qur'an sharpened into hostility, Imam Muslim sided with Imam Bukhari and abandoned Muhammad b. Yahya altogether. He was therefore a true disciple of Imām al-Bukhārī.

He wrote many books and treatises on Hadith, but the most important of his works is the collection (Jami’) of his Sahih. He originally named his book Musnad as-Ṣaḥīḥ, and mentioned in his book that he wrote authored such a book in response to a question from one of his students.

Imām Muslim meticulously collected 300,000 hadith and after a thorough examination of them retained only 4000, the genuineness of which were fully established. He prefixed to his compilation a very illuminating introduction, in which he specified some of the principles in which he had followed in the choice of his material. Imam Muslim has to his credit many other valuable contributions to different branches of Hadith literature, and most of them retain their eminence even to the present day. Amongst these Kitab al-Musnad al-Kabir 'Ala al-Rijal, Jami' Kabir, Kitab, al-Asma' wa'l-Kuna, Kitab al-Ilal, Kitab al- Wijdan are very important.

Imam Muslim strictly observed many principles of the science of Hadith, which had been slightly ignored by his great teacher Imam Bukhari (may Allah have mercy on both of them).

Imam Muslim considered only such traditions to be genuine and authentic as had been transmitted to him by an unbroken chain of reliable authorities up to the Prophet (ﷺ) and were in perfect harmony with what had been related by other narrators whose trustworthiness was unanimously accepted and who were free from all defects. He divided narrators and sub-narrators into 3 levels:
1. Those people who are completely authentic in their memory and character with no deficiency whatsoever. They were known to be honest and trustworthy.
2. People of slightly lesser memory and perfection than the previous category, yet still trustworthy and knowledgeable, not liars by any measure. Examples of people in this category include `Ata ibn Said and Layth ibn Abi Sulaim.
3. People whose honesty was a subject of dispute or even discussion. Imam Muslim did not concern himself with such people. Examples in this category include Abdullah ibn Maswar and Muhammad ibn Said al-Maslub.

Moreover, Imam Bukhari, while describing the chain of narrators, sometimes mentions their kunya and sometimes gives their names. This is particularly true in case of the narrators of Syria. This creates a sort of confusion, which Imam Muslim has avoided.

Imam Muslim takes particular care in according the exact words of the narrators and points out even the minutest difference in the wording of their reports. Imam Muslim has also constantly kept in view the difference between the two well-known modes of narration, haddathana (he narrated to us) and akhbarana (he informed us). He is of the opinion that the first mode is used only when the teacher is narrating the hadith and the student is listening to it, while the second mode of expression implies that the student is reading the hadith before the teacher. This reflects his utmost care in the transmission of a hadith. Imam Muslim has taken great pains in connecting the chain of narrators. He has recorded only that hadith which, at least, two reliable tabi'in (successors) had heard from two Companions and this principle is observed throughout the subsequent chain of narrators.

Sahih Muslim has been explained by Imam an-Nawawi and one of his teachers Abu `Amr ibn Salah.

His Students Imam Muslim had a very wide circle of students, who learnt Hadith from him. Some of them occupy a very prominent position in Islamic history, e.g. Abu Hatim Razi, Musa ibn Harun, Ahmad ibn Salama, Abu 'Isa Tirmidhi, Abu Bakr ibn Khusaima, Abu ‘Awana and Al-Dhahabi.

Imam Muslim lived for fifty-five years. He spent most of his time in learning Hadith, in its compilation, in its teaching and transmission. He always remained absorbed in this single pursuit and nothing could distract his attention from this pious task. He died in 261/875, and was buried in the suburbs of Nishapur.