What is the theme that Dostoyevski wishes to convey in Notes from the Underground?
I don't think that it's an easy theme that Dostoevski wishes to convey. Essentially, I think that he is suggesting that there is another side to what it means to be human. In Dostoevski's time, there was a belief that human beings are capable of great progress, enlightened thoughts and actions. Human progress and social perfectability were two logical results of this and the positivist philosophy that was being advocated all around him is where Dostoevski's starting point for his work lies.
Dostoevski's work speaks to the idea that there might not be an absolutist vision of human perfection. He is smart enough to know that such a vision totalizes all human consciousness and is transcendent. Thus, in creating his character, the Underground Man, Dostoevski has been able to puncture such an encompassing world view. Dostoevski seeks to bring out the idea that there might be destructiveness in both self and social forms within the human experience. Regardless of how much logic and "enlightened thought" may surround it, Dostoevski's construction of human nature is one in which consciousness is not geared towards anything elevated or anything in terms of social good. The Underground Man cares for little else except himself. He is not redemptive. He possesses no capacity to do anything else to wish pain on himself and others around him. Conveying this alienated and atomized construction of human identity is a major theme in the work. To present a character that is uniquely human in the worst of manners becomes Dostoevski's driving force.