Model theory is a branch of mathematical logic that studies the relationships between formal languages and their interpretations, or models. It focuses on how different structures can satisfy the same set of logical sentences, allowing mathematicians to explore the properties of these structures and the languages used to describe them. In model theory, a model is a mathematical structure that gives meaning to the symbols and sentences of a formal language. This field has applications in various areas, including set theory, algebra, and computer science, helping to understand the foundations of mathematics and the nature of mathematical truth.