The notation "GL(n, R)" stands for the General Linear Group of degree n over the real numbers. It consists of all n x n invertible matrices with real entries. An invertible matrix is one that has a non-zero determinant, meaning it can be used to solve systems of linear equations. The group operation in GL(n, R) is matrix multiplication, which combines two matrices to form a new matrix. This group is important in various fields, including linear algebra, geometry, and theoretical physics, as it describes transformations that preserve vector space structures.