A Linear Algebraic Group is a group of matrices that can be defined by polynomial equations. These groups combine concepts from both algebra and geometry, allowing for the study of symmetries and transformations in a structured way. They are important in various fields, including geometry, number theory, and representation theory. These groups can be thought of as a bridge between abstract algebra and linear algebra. They consist of sets of matrices that can be multiplied together and inverted, while also satisfying certain algebraic properties. Examples include GL(n), the group of invertible n x n matrices, and SL(n), the group of n x n matrices with determinant equal to one.