The albatross represents all three of these concepts: crime, punishment, and redemption.
The mariner's crime is the slaying of the beautiful albatross. The mariner has no reason to do this violent deed, yet he kill the bird anyway. The albatross had been a source of comfort and joy to the crew up until this point, so the murder was unwarranted.
This is how the mariner describes the albatross initially:
As if it had been a Christian soul,
We hailed it in God's name.
Until the albatross' death, the crew had treated it with kindness and given it food.
The albatross also is key in the punishment of the mariner. The bird is tied around the mariner's neck to remind him of his guilt. Death comes on a ship to take the entirety of the crew, except the mariner. This leaves him alone with the dead bodies of his shipmates and the body of the albatross. The mariner's shame is so thick, that he likens himself to the slimy things in life and is not able to pray.
And a thousand thousand slimy things
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