This book provides the Classification of Six dimensional solvable, indecomposable Lie algebras that have a five-dimensional nilradical. Such algebras were classified by the Russian mathematician G. M. Mubarakzyanov in a paper published in 1963. Depending on the structure of the five dimensional nilradical his paper has nine paragraphs. The paper contains errors because calculations were done by hand and the list of algebras is incomplete. Also some of his Lie algebras are isomorphic between themselves. MAPLE was used extensively with some routines to help finesse Mubarakzyanov’s list. Precisely, all the misprints were corrected and complete list of algebras was obtained: in Paragraph 6 he disregarded a case which gives two new Lie algebras. There is also one new Lie algebra in Paragraph 2, one in Paragraph 5 and two new Lie algebras in Paragraph 7.