A Motivating Problem -- to the Novikov and the Borel Conjecture -- Normal Bordism Groups -- The Signature -- The Signature Theorem and the Novikov Conjecture -- The Projective Class Group and the Whitehead Group -- Whitehead Torsion -- The Statement and Consequences of the s-Cobordism Theorem -- Sketch of the Proof of the s-Cobordism Theorem -- From the Novikov Conjecture to Surgery -- Surgery Below the Middle Dimension I: An Example -- Surgery Below the Middle Dimension II: Systematically -- Surgery in the Middle Dimension I -- Surgery in the Middle Dimension II -- Surgery in the Middle Dimension III -- An Assembly Map -- The Novikov Conjecture for ?n -- Poincaré Duality and Algebraic L-Groups -- Spectra -- Classifying Spaces of Families -- Equivariant Homology Theories and the Meta-Conjecture -- The Farrell-Jones Conjecture -- The Baum-Connes Conjecture -- Relating the Novikov, the Farrell-Jones and the Baum-Connes Conjectures -- Miscellaneous -- Exercises -- Hints to the Solutions of the Exercises.