Sahih Muslim is a collection of hadith book compiled by Imam Muslim ibn al-Hajjaj al Naysaburi. His collection is considered to be one of the most authentic collections of the Sunnah of the Prophet (May Allah honour Him and grant Him Peace), and along with Sahih al-Bukhari forms the "Sahihain," or the "Two Sahihs."
Al-Musnadu Al-Sahihu bi Naklil Adli
Imam Muslim's full name is Abul-Hussain Muslim ibn al-Hajjaj ibn Muslim ibn Warat al-Qushayri al- Naysaburi (206-261 AH/821-875 CE). Imam "Muslim," as his nasba shows, belonged to the Qushayr tribe of the Arabs, an offshoot of the great clan of Rabi'a. 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-sahih, and mentioned in his book that he wrote authored such a book in response to a question from one of his students.
Imam 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.
It contains roughly 4000 hadith (with repetitions) in 56 books. It shares about 2300 ahadith with Bukhari’s sahih.
Imam Muslim strictly observed many principles of the science of Hadith. Like Imam Bukhari, Imam Muslim too set a criteria for collecting ahadith. 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 (May Allah honour Him and grant Him Peace) 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.
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. 
- ‘Ilm al-hadeeth Knowledge/Study of the hadeeth
This means the wording the Prophet Muhammad (May Allah honour Him and grant Him Peace), used, its line of transmission and the original listener and/or recorder.
- ‘Ilm rijaal al-hadeeth Knowledge/Study of the credibility of transmitter
This means analysing the transmitters in terms of:
a. Faith: must be Muslim
b. Puberty: must have reached the age of maturity
c. Mental State: must be of stable mind
d. Sin: avoids sin; does not stray or deviate
e. Actions/Manners demonstrates an elevated standard of manners 
The six most authentic and distinguished books of ahadith that are taught and learned in Islamic Studies are:
ii) Sahih Muslim
iii) Jama’i at-Tirmidhi
vi) Sunan Nasa’ii
vi) Sunan ibn Majah
Among the most Authentic books of Ahadith, Sahih Al Bukahri considered to be one of the most authentic collections of the Sunnah of the Prophet Muhammad (May Allah honour Him and grant Him Peace), and along with Sahih Al Mulsim forms the "Sahihain," or the "Two Sahihs."
  http://sunnah.com/muslim/about