Linear algebraic groups are mathematical structures that combine concepts from both algebra and geometry. They are groups of matrices that can be defined by polynomial equations, allowing for the study of symmetries and transformations in a linear space. These groups can be classified into various types, such as abelian groups and reductive groups, based on their properties. These groups play a significant role in various fields, including number theory, representation theory, and geometry. They provide a framework for understanding how algebraic objects can be transformed and related to one another, making them essential in modern mathematics and theoretical physics.