  This thesis was concerned with classifying the real indecomposable solvable
Lie algebras with codimension one nilradicals of dimensions two through seven.
This thesis was organized into three chapters.
  In the first, we described the necessary concepts and definitions about Lie
algebras as well as a few helpful theorems that are necessary to understand the
project. We also reviewed many concepts from linear algebra that are essential
to the research.
  The second chapter was occupied with a description of how we went about
classifying the Lie algebras. In particular, it outlined the basic premise of
the classification: that we can use the automorphisms of the nilradical of the
Lie algebra to find a basis with the simplest structure equations possible. In
addition, it outlined a few other methods that also helped find this basis.
Finally, this chapter included a discussion of the canonical forms of certain
types of matrices that arose in the project.
  The third chapter presented a sample of the classification of the seven
dimensional Lie algebras. In it, we proceeded step-by-step through the
classification of the Lie algebras whose nilradical was one of four
specifically chosen because they were representative of the different types
that arose during the project.
  In the appendices, we presented our results in a list of the multiplication
tables of the isomorphism classes found.
