A Transfer Function is a mathematical representation that describes the relationship between the input and output of a linear time-invariant system. It is typically expressed as a ratio of two polynomials in the Laplace transform variable, s. The transfer function helps engineers analyze system behavior, stability, and frequency response. In control systems, the transfer function is crucial for designing and understanding systems like electrical circuits, mechanical systems, and signal processing. By examining the transfer function, one can predict how a system will respond to various inputs, making it an essential tool in fields such as control engineering and signal processing.