Madara's Abilities

Most of Madara's abilities are still unknown. He is known to have an advanced Mangekyo Sharingan, and to make use of space-time ninjutsu speculated by Kakashi to be even greater than the Fourth Hokage's space-time ninjutsu. Since the Uchiha clan is known for its fire techniques, it is also speculated that he knows advanced fire techniques as well. He was armed with a giant fan during the time of Konoha's founding, which may explain the origin of a paper fan being the symbol of the Uchiha clan. He and Deidara were able to defeat the Three Tails, but Madara (as Tobi) was never shown doing anything but running away from it. After the battle, which goes largely unwitnessed, he claims to have knocked it out with a single attack. Deidara disagrees with the assessment, claiming that it was his "artistic contribution" (exploding clay) that allowed them to win. While as Tobi, Madara is also shown planting Deidara's clay minefields underground during a later battle. Itachi refers to Madara as being an "invincible immortal", which is further evidenced by continued existence despite his advanced age and his surviving the battle at the Valley of the End despite witnesses belief that he died.
Madara shows the ability to recover from what are presumably debilitating or fatal blows. After being slashed across the midsection by Sasuke's sword, he collapses, only to stand up again a few seconds later and complain about the speed of the attack, and later when Naruto hits him in the back with a Rasengan. The attacks literally phase through him, avoiding damage. He is also seen being hit by Sasuke's Amaterasu but emerging unharmed.
Madara also shows the ability to travel long distances within relatively short timespans, escaping the final explosion created by Deidara and reappearing in Amegakure, then travelling to the Valley of the End all within a very short time span. It is speculated by Kakashi and Sakura that he uses space/time ninjutsu to instantly send himself or even parts of his body to different locations or some sort of void and instantly bring them back. This was noted in his fight with Naruto, Sakura, Sai, Kakashi, Yamato, Kiba, Hinata, and Shino when Naruto attacked with a full powered Rasengan that phased right through him, and also when he escaped Shino's bugs even though they were completely surrounding his body. Second, when Madara criticized Zetsu's slow speed, Zetsu responds with a remark implying that his jutsu enables him to move at very high speeds.
After he escaped Deidara's final explosion, it is revealed that he possesses the Sharingan, shown visible through the opening of his mask. The demon fox mentioned that Madara's chakra was sinister, more sinister than its own. Madara was the only person capable of taming the demon fox which was said to only come where human malice collects and festers, yet he was able to use the Sharingan to tame the tailed beast.
During Itachi's fight with Sasuke, it is revealed that Madara Uchiha and his younger brother were the first members of the Uchiha to activate the Mangekyo Sharingan, and used its power to take over the clan. After implanting his brother's eyes into his own body, Madara then awakened a new "eternal" Mangekyo Sharingan, a combination of his own and his brother's Mangekyo Sharingan which gave him untold amounts of power without the risk of losing his eyesight. It was with this power Madara was able to forcibly subdue the demon fox. He is said to be the strongest Uchiha.