Description: This note explains the following topics: Basic definitions and examples, Theorems of Engel and Lie, The Killing form and Cartan s criteria, Cartan subalgebras, Semisimple Lie algebras, Root systems, Classification and examples of semisimple Lie algebras.

Description: This note is aimed at the engineering or scientific professional who wishes to learn about Fractional Calculus and its possible applications in his/her field of study. The intent is to expose the reader to the concepts, applicable definitions, and execution of fractional calculus and second to show how these may be used to solve several modern problem.