Abstract: In this talk we will give an introduction into algebraic L-Theory. This is an invariant of rings with involution $$(R,\sigma)$$. One has an L-theory spectrum $$L(R,\sigma)$$ and the homotopy groups are called the L-groups, which can also be indepently described and are related to classical Witt-groups. There is a close relation between L-theory and K-theory that has been exploited in recent work in arithmetic situation. We will explain how the relation generally works. Specifically in the case of $$C^*$$-algebras one also comparisons between topological K-theory and algebraic L-theory which I will explain. The latter is based on joint work with M. Land and M. Schlichting.