Wa Alaikum salaam wa Rahmatullahi wa Barakatuh. I like to know about what is Abu talib's real in hadith sources and was he a muslim or no ?

Alaikumassalam wa rahmatullah wa barakatuh,

Authentic narrations mention that Abu Talib was not a Muslim and that he did not convert to Islam even at his death bed. Here is a relevant hadith from Sahih al-Bukhari:

When the time of the death of Abu Talib approached, Allah's Messenger (ﷺ) went to him and found Abu Jahl bin Hisham and `Abdullah bin Abi Umaiya bin Al-Mughira by his side. Allah's Messenger (ﷺ) said to Abu Talib, "O uncle! Say: None has the right to be worshipped but Allah, a sentence with which I shall be a witness (i.e. argue) for you before Allah. Abu Jahl and `Abdullah bin Abi Umaiya said, "O Abu Talib! Are you going to denounce the religion of `Abdul Muttalib?" Allah's Messenger (ﷺ) kept on inviting Abu Talib to say it (i.e. 'None has the right to be worshipped but Allah') while they (Abu Jahl and `Abdullah) kept on repeating their statement till Abu Talib said as his last statement that he was on the religion of `Abdul Muttalib and refused to say, 'None has the right to be worshipped but Allah.' (Then Allah's Messenger (ﷺ) said, "I will keep on asking Allah's forgiveness for you unless I am forbidden (by Allah) to do so." So Allah revealed (the verse) concerning him (i.e. It is not fitting for the Prophet (ﷺ) and those who believe that they should invoke (Allah) for forgiveness for pagans even though they be of kin, after it has become clear to them that they are companions of the fire (9.113). (Sahih al-Bukhari 1360)