Both Darwin and Freud influenced The Strange Case of Dr. Jekyll and Mr. Hyde by Robert Louis Stevenson, as their theories underlie the notion of the split personality we find in the story.
From a Darwinian perspective, modern humanity very gradually evolved from other primates. On a social level, Darwin and other thinkers who accepted his theories often felt that humanity itself went through evolutionary stages progressing from savages and brutes to the great civilizations of western Europe. From this perspective, Mr. Hyde would represent humanity at an earlier stage of evolution, before it developed higher forms of morality.
From a Freudian perspective, there are three main components to the human psyche, the id, ego, and superego. The id is the part that has primal desires and the superego internalizes societal constraints and morality. In most people, the two are in conflict with the superego restraining the desires of the id. In Stevenson's story, Jekyll would represent the superego and Hyde the id.