a paternal uncle of Muhammad, and the father of Ali, the 4th caliph who is also the son-in-law of Muhamamd.
Abu Talib took care of Muhammad after his mother Aminah and grandfather Abdul Muttalib died. Muhammad was greatful for all that Abu Talib and his wife Fatima bint Asad did for him. Abu Tali took Muhammad with him on business trips as far as Syria. As a result Muhammad had many opportunities to learn of the many different cultures and religions in his travels. From Sahih Bukhari 5.185, we see that Abu Talib was an influential man among the Quraysh.
He protected Muhammad while he was alive and died a pagan. At his death, Muhammad prayed for him.
Narrated Al-Musaiyab:Muhamamd claimed that Abu Talib is spared the bottom of Hell Fire because of him:When Abu Talib was in his death bed, the Prophet went to him while Abu Jahl was sitting beside him. The Prophet said, "O my uncle! Say: None has the right to be worshipped except Allah, an expression I will defend your case with, before Allah." Abu Jahl and 'Abdullah bin Umaya said, "O Abu Talib! Will you leave the religion of 'Abdul Muttalib?" So they kept on saying this to him so that the last statement he said to them (before he died) was: "I am on the religion of 'Abdul Muttalib." Then the Prophet said, " I will keep on asking for Allah's Forgiveness for you unless I am forbidden to do so." Then the following Verse was revealed:--
"It is not fitting for the Prophet and the believers to ask Allah's Forgiveness for the pagans, even if they were their near relatives, after it has become clear to them that they are the dwellers of the (Hell) Fire." (9.113)
The other Verse was also revealed:-- "(O Prophet!) Verily, you guide not whom you like, but Allah guides whom He will ......." (28.56) (Sahih Bukhari 5.223. also Sahih Bukhari 2.442, Sahih Bukhari 6.197, Sahih Bukhari 6.295)
Narrated Al-Abbas bin 'Abdul Muttalib:In another hadith, however, Muhammad was not so sure, but instead was only hoping that his intercession will allow Abu Talib to escape worst punishment:That he said to the Prophet "You have not been of any avail to your uncle (Abu Talib) (though) by Allah, he used to protect you and used to become angry on your behalf." The Prophet said, "He is in a shallow fire, and had It not been for me, he would have been in the bottom of the (Hell) Fire." (Sahih Bukhari 5.222. also Sahih Bukhari 8.227)
Narrated Abu Said Al-Khudri:That he heard the Prophet when somebody mentioned his uncle (i.e. Abu Talib), saying, "Perhaps my intercession will be helpful to him on the Day of Resurrection so that he may be put in a shallow fire reaching only up to his ankles. His brain will boil from it." (Sahih Bukhari 5.224. also Sahih Bukhari 8.569)
Narrated 'Abdullah bin Dinar:Although believers are not allowed to inherit properties of unbelievers, yet Ali and Talib inherited his properties:My father said, "I heard Ibn 'Umar reciting the poetic verses of Abu Talib: And a white (person) (i.e. the Prophet) who is requested to pray for rain and who takes care of the orphans and is the guardian of widows." Salim's father (Ibn 'Umar) said, "The following poetic verse occurred to my mind while I was looking at the face of the Prophet (p.b.u.h) while he was praying for rain. He did not get down till the rain water flowed profusely from every roof-gutter: And a white (person) who is requested to pray for rain and who takes care of the orphans and is the guardian of widows . . . And these were the words of Abu Talib." (Sahih Bukhari 2.122)
Narrated 'Amr bin 'Uthman:Usama bin Zaid said during the Conquest (of Mecca), "O Allah's Apostle! Where will we encamp tomorrow?" The Prophet said, "But has 'Aqil left for us any house to lodge in?" He then added, "No believer will inherit an infidel's property, and no infidel will inherit the property of a believer." Az-Zuhri was asked, "Who inherited Abu Talib?" Az-Zuhri replied, "Ali and Talib inherited him." (Sahih Bukhari 5.579. see also Malik's Muwatta 27.27.12.10)