Hadith
The reported sayings and actions of Muhammad, the second source of Islamic law, and the most contested body of text in the Muslim world.
A hadith is a report of something the Prophet Muhammad said, did, or silently approved. Together the hadith constitute the Sunnah, the Prophet's example, which is the second source of Islamic law after the Quran, and in practice the more detailed one. The Quran instructs Muslims to pray but does not describe how; the hadith do. Almost every specific rule in Islamic law, and almost every modern argument about what Islam requires, is an argument about hadith.
Anatomy of a report
Every hadith has two parts. The isnad is the chain of transmission, a list of names running backward from the person telling you to an eyewitness: I heard from A, who heard from B, who heard from C, who heard the Prophet say. The matn is the content itself, usually a sentence or two.
The isnad is the intellectually remarkable part. Muslim scholars built an entire science around it, compiling biographical dictionaries of tens of thousands of transmitters and grading each one for memory, honesty, and whether they could plausibly have met the person they claimed to quote. A report from a known exaggerator, or one whose chain requires two men to have met when they lived in different cities in different decades, gets downgraded regardless of how pious its content sounds.
The grading system that came out of this has four rough levels: sahih, sound; hasan, good; da'if, weak; and mawdu', fabricated. That last category exists because fabrication was rampant. In the first two centuries of Islam, political factions, storytellers, and sectarian partisans all had reasons to put words in the Prophet's mouth, and everyone knew it. Hadith criticism was invented as a defense.
The collections
The great compilations were made in the ninth century, roughly two hundred years after Muhammad's death. Muhammad al-Bukhari, who died in 870, is said to have sifted some 600,000 reports and retained around 7,300 including repeated chains, which comes to somewhere between 2,600 and 2,800 distinct traditions depending on how you count. His collection and that of his contemporary Muslim ibn al-Hajjaj are the two most authoritative books in Sunni Islam after the Quran itself. Four other collections complete the Sunni canon, the Kutub al-Sittah or Six Books.
Shia Islam has its own canon, the Four Books compiled in the tenth and eleventh centuries, which includes traditions transmitted through the Imams and treats with suspicion reports carried by Companions whose later conduct Shia consider problematic. Two traditions can therefore reason identically and reach different conclusions, because they are working from different source material.
Why it is the live fault line
Every major fight in modern Islam runs through hadith.
Salafi and Wahhabi movements built their program on returning to the Quran and authentic hadith directly, bypassing the accumulated interpretive tradition of the legal schools. Militant groups justify tactics by producing hadith, and their opponents answer by attacking the chains or the context. Reformists argue that many of the harshest rulings on women, apostasy, and non-Muslims rest on single-chain reports that never had strong authentication and that hardened into orthodoxy through repetition. A small Quranist minority rejects hadith as a source of law altogether, which mainstream scholars of every school consider a rejection of Islam as historically practiced, because without hadith there is no practical guidance on how to do almost anything the Quran commands.
Western historians have run their own argument since the nineteenth century over whether the isnad system can bear the weight placed on it, given that it authenticates transmitters rather than the moment of origin, and that the collections were made two centuries after the fact. Muslim scholars answer that the biographical apparatus is far more rigorous than anything comparable in the ancient world, which is also true.
The practical upshot for anyone reading about Muslim politics is simple. When two sides quote the Prophet against each other, they are not disagreeing about faith. They are disagreeing about the authenticity of specific texts, and that dispute has been running, professionally and in detail, for twelve hundred years.