Talks at ``Spring school on Index theory, Lie groupoids and boundary value problems'' Regensburg, March '09, Ammand and Bunke organizers

• The first lecture was a general overview of the connections between analysis on singular spaces, analysis on non-compact manifolds, and Lie manifolds. Some applications to numerical methods (Mechanics, Finance, ... ) were also mentioned. I used the blackboard for this lecture.
• Lectures 2 and 3, on Lie manifolds, their geometry (metric, connection, curvature), Fredholm conditions for geoemtric operators, and Lie groupoids.
• Lecture 4, on applications to well-posedness of elliptic equations (including Elasticity) on polyhedral domains and optimal rates of convergence for the Finite Element Method on polyhedral domains.
• Lecture 5, on integration of Lie algebroids, index theory for Lie manifolds, and Schroedinger operators