Various biological functions originate from temporal changes in the activity of biomolecules, especially genes. In this chapter, we will consider how biomolecules exhibit temporal changes under the regulations of activation and repression. Mathematical methods for dealing with temporal changes, or dynamics, have been developed in the field of dynamical systems theory, and a variety of analytical methods are available. In order to understand the basic concepts of mathematical analysis, this chapter first focuses on the activity of a single molecule and then considers its dynamics.