These notes were developed from a course taught at Rice Univ- sity in the spring of 1976 and again at the University of Hawaii in the spring of 1977. It is assumed that the students know some linear algebra and a little about differentiation of vector-valued functions. The idea is to introduce students to some of the concepts of Lie group theory-- all done at the concrete level of matrix groups. As much as we could, we motivated developments as a means of deciding when two matrix groups with different definitions are isomorphic. In Chapter I group is defined and examples are given ho- morphism and isomorphism are defined. For a field k denotes the algebra of n x n matrices over k We recall that A E Mnk has an inverse if and only if det A 0, and define the general linear group GLn, k We construct the skew-field lli of to operate linearly on llin quaternions and note that for A E Mnlli we must operate on the right since we mUltiply a vector by a scalar n on the left. So we use row vector