Lie algebras are efficient tools for analyzing the properties of physical systems concrete applications comprise the formulation of symmetries of hamiltonian systems the description of atomic molecular and nuclear spectra the physics of elementary particles and many others this work gives an. This work gives an introduction to the properties and the structure of the lie algebras sun first characteristic quantities such as structure constants the killing form and functions of lie. Introduction lie algebras are efficient tools for analyzing the properties of physical systems concrete applications comprise the formulation of symmetries of hamiltonian systems the description of atomic molecular and nuclear spectra the physics of elementary particles and many others. This work gives an introduction to the properties and the structure of the lie algebras sun first characteristic quantities such as structure constants the killing form and functions of lie algebras are introduced the properties of the algebras su2 su3 and su4 are investigated in detail geometric models of the representations are developed a lot of care is taken over the use of the term multiplet of an algebra the book features an elementary matrix access to sun