The present book is an outcome of my course on Riemannian Geometry. Its origin can be traced back to a series of special lectures which I gave during the summer semester 1961 in Bonn. At that time, D. Gromoll and W. Meyer were among my students and in 1967 we jointly published in the Lecture Notes Series our "Riemannsche Geometrie im GroBen".
These lectures have met with great interest, because for the first time a concise introduction into Riemannian Geometry wa& combined with global methods culminating in the so-called Sphere Theorem, which states that the underlying topological manifold of a simply connected Riemannian manifold with suitably restricted positive curvature is a sphere.