Philosopher's Stone

The Philosopher's Stone (賢者の石, Kenja no Ishi), also known by various other names such as the Red Stone, the Fifth Element, and more, is a powerful transmutation amplifier appearing in both the anime and manga. Due to the absolute law of alchemy being equivalent exchange, the stone gives the illusion that someone is able to override that law. Being that it is an illusion, the powers of the stone itself are not unlimited, and only appears to allow an alchemist to bypass equivalent exchange as long as the stone retains its power. Many of the main events in the series revolve around the Elric brothers' attempts to obtain this stone, in order to gain their original bodies, of whom had to be paid to Truth in accordance to the laws of alchemy.

Composition of the Philosopher's Stone
It is never explained in the series the exact process of creating a Philosopher's Stone, but it is known that human souls of ones who have passed can be trapped and condensed with certain transmutation circles. These thousands or perhaps millions of souls make up both the power and physical existence of a Philosopher's Stone. It is a frequent misconception that the properties of the stone itself allow someone to override the law of equivalent exchange, but this perception is simply an illusion. The power of the Philosopher's Stone allows one to perform feats greater than what one can do naturally, but the stone gets weaker every time it's used because that power comes from souls, which get consumed in these transmutations. When all the souls have been destroyed, the stone also ceases to exist. The raw material of Philosopher's Stone is a very large number of human lives, ranging from only one human life, to a few dozen, to a few million, or perhaps even more.

It is rumored that the Philosopher's Stone can allow one to complete a human transmutation. However, the abilities that can be performed can range from the completely equal resurrection of another human, to the worthless repairing of an inanimate object.

Physical appearance
The Philosopher's stone can take many forms, ranging from a lumpy, coal-like rock to a viscous liquid, as with the one that Dr. Marcoh owns or even as a man (ex.: Hohenheim). Their color in the purely material form is always a dark, blood-like red. Usually the smaller it is, the less powerful the Philosopher's Stone.

History
The first stone in history was transmuted by the original homunculus later known as "Father", using the souls of the people of Xerxes. This event inspired the legend of a country which was destroyed in a single night. The later Philosopher's Stones were transmuted by Doctor Tim Marcoh and his fellow alchemists who were instructed to make the Stones by Lust and the other Homunculi, using the lives of Ishvalan prisoners, and later the makers themselves to cover it up. This series of Philosopher's Stones wasn't complete - they were made from only about 13 prisoners (based on the count shown in chapter 59). In the manga, the stone that Father Cornello used was also one of this series.

Generally believed to exist only in legend, the Philosopher's Stone has long been sought by alchemists as the ultimate goal of their craft. While alchemy is an amazing preternatural art in and of itself, its scientific limitations are such that the dream of a mystical and mythical object capable of eradicating those limits is one shared by generations of practitioners. Though, in more pragmatic times, the legend of the Philosopher's Stone has come to exist only in the fanciful illusions of Romantics, the fabled amplifier is, in fact, an arcane reality.

In the 2003 Anime series, the first known stone was created by Hohenheim of Light and Dante around 400 years prior to the series. Both alchemists used the power of the stone to transfer their souls from their original bodies to others throughout the course of four centuries in an effort to live eternally. The stone latter erodes away after Dante drains the last of its power to transfer into Lyra's body, causing a Rebound that accelerates the decayment of the vessel, and thus, she desperately seeks the stone embedded in Alphonse Elric's armor body to continue living.

There are also 'imitation' stones in that series, known as a Red stone.

In the manga/Brotherhood tie-in movie Fullmetal Alchemist: The Sacred Star of Milos, both Creta and Amestris have had soldiers fighting for control of Table City and the rest of the land of Milos for centuries over rumors that a Philosopher's Stone was in the city. At the same time, one of the legends of power that the Milosian people seek to harness to reclaim their independence is an object called the Sanguine Star. Ultimately, both these objects turn out to be referencing the same thing, as the Sanguine Star is actually a variant of the Philosopher's Stone which seemingly relies on many lives' worth of blood rather than actual souls for its creation making a humane but slow way of creating the Star possible. In fact, when Julia Crichton prepares to swallow a newly created Star, Ed warns her that it will consume her soul, which indicates a similar basis within the Star itself for deriving power from souls. He also states that the Sanguine Star which Ashleigh Crichton swallowed (to save his life) is warping Ashleigh's soul. It is only after both Crichtons regurgitate the Stars they swallowed that the brother and sister return to their own sense of self.

Trivia

 * It is interesting to note that in the manga/2009 anime, Van Hohenheim, being a human Philosopher's Stone, seemed to be able to use more power from his stone than anyone else, due to having individualized each and every one of the 536,329 souls within himself. The power seemed to be so great that Van was able to block several energy blasts from Father after the latter had absorbed God, which impressed Father.
 * This could indicate that while the souls inside the stones are able to amplify alchemic abilities, when the souls are individualized, the energy that each soul willingly share are of a much greater quality than if they were as a mass collection of souls with no true wills.
 * In the 2003 anime, although Dante says at one point that she didn't know how to make a Philosopher's Stone, this could very well be a lie. It is more than likely that she was simply unwilling to try because of the risks involved when she saw Hohenheim craft the first one.