This seminar introduces its participants to the basic structure theory and classification of Lie algebras, focusing on characteristic 0. Participants prepare and present lectures on the following topics:

1. Levi's theorem about the decomposition into solvable and semi-simple Lie algebras
2. Structure of solvable Lie algebras and in particular Engel's theorem representing them by upper triangular matrices
3. Structure of simple Lie algebras, and in particular the notion of a Cartan subalgebras
4. Classification of complex simple Lie algebras
5. Ado's theorem, showing that every finite dimensional real Lie algebra is a Lie algebra of matrices

A lecture plan will be discussed during the first meeting.