Speaker : Helke Karen Hesse Abstract: An Introduction to Projective Newton Methods In this talk an introduction to projective Newton methods will be given. We will start with the Newton Method in finite dimensional space, will then consider the Newton method in function space and will proceed with the consideration of discretisation and choice of finite dimensional subspaces. This will lead to the formulation of the projective Newton method. Convergence results will shortly be summarized, and in the framework of adaptivity for projective Newton methods we will take a look on inexact Newton methods and will shortly sketch the idea of stepwise grid adaption.