Basic properties of lie groups and lie algebras

In this thesis, manifold concept is explained and some basic examples are given. On the manifold structure, the fundamental theorems are used and proved to be used in Lie Group and Lie Algebra structure. The definition of Lie Group is expressed and the tangent space of a Lie group in the identity and its properties are examined and examples are given. Bracket operation was given on the tangent space of a Lie group and Lie Algebra was constructed on the tangent space. Some basic Lie group examples and Lie Algebras of these groups are discussed.