In these lectures, we study Lie groups and their Lie algebras, mostly from a differential geometric point of view.
Our goal is the correspondence between (finite dimensional) Lie algebras and simply connected Lie groups.

- As a warmup, we start with 'matrix Lie groups' and 'matrix Lie algebras'; the concrete and maybe already known examples.
- Then we study abstract Lie algebras and prove that any abstract (finite dimensional) real Lie algebra is a matrix Lie algebra (Ado's theorem).
- We define and study Lie groups and show Lie's 3 theorems. For this, we'll go quickly over the theory of regular foliations on smooth manifolds.

Note that for the third and last part of the lectures, you will need solid background knowledge in the following differential geometry prerequisites: smooth manifolds and smooth maps, tangent bundles and tangent maps, vector fields and flows. If you haven't this knowledge, it is strongly recommended that you follow in parallel the lectures on differential geometry.