Rodion, is Raskolnikov's first name. On the bottom, you see "Раскол", romanized as Raskol. In the note in means the word "split". A fitting thing. Along with the axe. Raskolnikov, in first part of the book, is split. Mentally, he is in a state of severe anxiety, delusion, and bewilderment. He is torn over whether or not he should kill the old pawnbroker. He desires company and solitude; he loathes himself and puts himself into a pedestal. Everything, to him, seems like a fever. He justifies committing a senseless murder by creating excuses; he creates one when he hears two men, a soldier and another man, talking about how the old pawnbroker has a lot of wealth, and if someone kills her, her wealth can be given to those in need. This is his justification. He is in a dream, returned to his poverty-stricken village, stumbling into a bar. He sees drunken men, ravenously beating a man's horse, with the owner letting it be abused. Raskolnikov tries to save it, but his father restrains him, because all the men are drunken and he should not mess with them and their actions. He sees himself in the men, and the crime he is to commit. He is both the witness and the criminal, in one, torn. He figures out that the main reason why people are always caught in crime is that they lose their sense of reason, consumed in guilt and shame before they commit a crime, and after it as well; he dismisses it, putting it aside as he believed that the deed he was about to do was not a crime in intention, but he believed it was a good deed with very little mental effects beforehand. Well, as time passed, he waited to commit the murder.

As you can see here, Rodion carries an axe. Well, Raskolnikov decided to use it as his weapon of choice. It was already clear to him what his weapon would be, since the aforementioned dream in his home village. He goes inside a tradesman's workshop, and takes an axe, and hides it in his coat. He gets somewhat ill before he commits the crime, presumably because of his mental state at the time. He then sneaks off, and goes into the old pawnbroker's residence. She was alone at the time. He speaks to her, giving her a box. He soon has her trapped. He is under a great state of stress, and is hesitating, but he kills her, by hitting her in the head with the blunt side of the axe. He soon finds the pawnbroker's younger sister-in-law, and kills her, this time with the sharp side of the axe. He, despite his expectations, loses his ability to reason, temporarily. He tries to clean off everything, but he finds men, looking for the poor pawnbroker, just to find her dead. He runs off, back to where he staying at, and they spot him, but never caught him. He returns the axe, after cleaning it. Soon, when he goes to his place of lodging, he is paranoid as hell, worrying about whether or not there were bloodstains on his shoes, his coat, any o his clothing. He is consumed with a burden of guilt, with the weight of Hell and Earth on his shoulders, as he convinces himself to surrender to the police. He "faces the sin".

While I'm not particularly fond of Limbus Company, this is awesome.

(My explanation got all the way to the middle of Part Two, Chapter 1. That's all I've read so far, if I got anything wrong, tell me. I pulled it out of memory.)