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.
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