Atoning for past mistakes is a major theme in Fullmetal Alchemist: Brotherhood, and no one embodies that more than the Elric brothers.
Edward and Alphonse grew up in Resembool with their mother Trisha Elric and their wandering father, Van Hohenheim, meaning the young brothers were much more attached to Trisha than their father. When Trisha died of a local plague, the brothers resolved to use their alchemy skills to reverse death and put things back where they wanted them. But things didn't go as planned.
Getting Ready
Once Trisha passed, Ed and Al's grief soon gave way to grim resolve. The boys were budding scientists and trained alchemists, and they saw everything in the world as an equation to solve. For them, there was no problem that couldn't be solved with transmutation circles and formulas, and they believed that a dead parent was just another scientific challenge. In secret, Ed and Al began a long research project to devise a method for human transmutation, and this consumed all their waking hours.
Winry, their neighbor and friend, could tell that the brothers were up to something, but wasn't privy to the doomed plans of her friends. One day, Ed and Al finished devising the necessary formula and transmutation circle for their project, and they bought all the raw ingredients for a human body: carbon, calcium, phosphate, gold, lime and much more. The brothers then placed these raw materials in a tray in the middle of a huge transmutation circle, offered drops of their blood to provide DNA and placed their hands on the circle to complete the project.
Equal Exchange With The Truth
The transmutation circle glowed at once, but the brothers could soon tell that something was off. A strange power awakened...and then seized both brothers, tearing their bodies apart. Alphonse's whole being dissolved before Ed's eyes, and once Al was gone, Ed found himself in a blank white space that looked nothing like his basement. He was confronted by a faceless figure calling itself The Truth, and it explained that the brothers had knocked on a very special door: the door to the truth of all things. Now Edward was dragged inside to learn a lesson.
Within that gate, Ed had all kinds of information about reality wildly flung into his brain, and once it stopped, he was told that he must pay the "toll" for that arcane knowledge: his left leg. Everything comes at a price, the Truth told him, and the Elric brothers had stumbled upon this exchange without even realizing it. Ed was put back in the basement, his leg missing and his body wracked with pain. Alphonse was totally gone, but Ed couldn't accept that. He bandaged himself, then drew another alchemic symbol on a suit of armor and transmuted Al's soul to save him. He came before the Truth once again, and gave his right arm in exchange for his brother's soul, binding it to the armor. Now the brothers were mangled from a lesson they had never intended to learn, and their mother was certainly not back from the dead. It was impossible to revive her.
Trisha Elric was gone for good, and her sons learned a hard lesson for a horrific price.