Volterra equations are integral equations that describe a relationship between a function and its integral over a variable range. They are named after the Italian mathematician Vito Volterra, who introduced them in the early 20th century. These equations can be classified into two main types: Volterra integral equations of the first kind and Volterra integral equations of the second kind, depending on how the unknown function appears in the equation. These equations are commonly used in various fields, including physics, biology, and engineering, to model dynamic systems and processes. They can represent phenomena such as population dynamics, where the growth of a species depends on its past population, or in control theory, where the current state of a system is influenced by its history.