Bull: He describes the normal, "stupid" person as an enraged bull rushing headlong into a wall at the slightest impulse. This man, this spontaneous man, or man of action is ridiculed and despised by the Underground Man throughout his Notes, though he admits that he often envies him.
Mouse: The UM sees himself as this creature because of his hyperconsciousness. He likens himself to a mouse because a mouse is the antithesis of a normal man, or bull. While the bull acts on its rather simple mental reasoning, the mouse cannot act because its overly sophisticated mental processes perpetually plague it with doubt and vacillation, rendering it unable to do anything, save "creep ignominiously back into its mousehole."
Underground: This hole, this underground, is the home of the UM and those like him. It is compared to a mousehole in one of the chapters, though usually he refers to it as his corner. Yet the underground is more than a physical place of isolation; it's a psychological hang-up as well. Possessing the overly sensitive and sheltered consciousness of the underground, the UM finds himself unable and unwilling to meaningfully interact with others, despite his ardent desire to do just that.
Wall: The wall represents, the Underground Man explains, "the laws of nature, the conclusions of natural science and mathematics." The wall also embodies such ideas as evolution, which Dostoevsky largely equated with atheism and socialism. While the man of action readily accepts the wall and its implications, the UM (and Dostoevsky) couldn't come to grips with the concept of the stone wall, the idea that "two times two makes four," because it makes man out to be an animal-a mere phenomenon of science, lacking the human component of free will.
Crystal Palace, Organ stop, Piano key: Not dissimilar to the wall metaphor, these symbols represent the determinism Dostoevsky fought to escape. The crystal palace, namely, was Chernyshevsky's utopian model for human happiness, where the whole world ran according to reason, like a clock. The organ stop and piano key are metaphors the UM says man would be reduced to under such a "utopian" vision. Man would have no free will, and therefore would behave as if someone were playing his key on the piano.