This book aims to provide a friendly introduction to non-commutative geometry. It studies index theory from a classical differential geometry perspective up to the point where classical differential geometry methods become insufficient. It then presents non-commutative geometry as a natural continuation of classical differential geometry. It thereby aims to provide a natural link between classical differential geometry and non-commutative geometry. The book shows that the index formula is a topological statement, and ends with non-commutative topology.From Differential Geometry to Non-commutative Geometry and Topology is written by Neculai S. Teleman and published by Springer. ISBNs for From Differential Geometry to Non-commutative Geometry and Topology are 9783030284336, 3030284336 and the print ISBNs are 9783030284329, 3030284328.