Contents : An Introduction to Lie Groups ,Representations of Lie Groups ,Introduction to Lie Algebras and TheirRepresentations , Monotileable Amenable Groups: An Application , Lie Algebra of Infinitesimal Generators of theSymmetry Group of the Heat Equation , A Note on the Lie Algebra of the Invariants in the CBS Nonlinear Equation, Root Systems Lie Algebras , Spherical Functions on Fuzzy Lie Group , Discussion on the Homology Theory of Lie Algebras , Representations of Ten-Dimensional Levi Decomposition Lie Algebras , On Two Classes of Extended 3-Lie Algebras