Table of Contents

Basic definitions.- Representations of nilpotent algebras.- Cartan subalgebras.- The killing form.- The cartan decomposition.- Systems of fundamental roots.- Dynkin diagrams.- Some astronomical observations.- Algebras with a given star.- Subideals, derivations, automorphisms.- The bear radical.- Other radicals.- Baer— fitting.- Lie algebras in which every subalgebra is a subideal.- The minimal condition for subideals.