The Prophet's lineage is clearly documented in books of history; every one of his fathers is known all the way back until `Adnan. And even though the historians disagree about the names of `Adnan's forefathers, they agree that `Adnan - and by extension the Prophet (peace be upon Him) - was a direct descendant of the Prophet Ibrahim (peace be upon him).
Keeping in mind that the word "ibn" means "son of". Here then the full name of the Prophet Muhammad (peace be upon Him).
Muhammad ibn `Abdullah ibn `Abdul-Muttalib ibn Hashim ibn `Abd-Manaf ibn Qusai ibn Kilab ibn Murrah ibn Ka'ab ibn Luaiy ibn Ghalib ibn Faihr ibn Malik ibn An-Nadr ibn Kinanah ibn Khuzaimah ibn Mudrikah ibn Ilyas ibn Mudar ibn Nizar ibn Mu`idd ibn `Adnan
[Al-Bukhari (along with ibn Hajar's famous conmmentary, Al-Fath), the Book of the Ansar's Virtues; chapter, "The Sending of the Prophet (peace be upon Him)," before hadith number: 3851]