Historically, bounded cohomology has its roots in the cohomology of Banach algebras (after B.E. Johnson). M. Gromov turned it into a powerful and versatile tool in geometry and group theory. Lately, bounded cohomology has found applications in non-commutative measure theory, being a central tool for certain orbit equivalence rigidity results.
This lecture will present a leisurly and non-specialized introduction to bounded cohomology. We will highlight its connection to topics such as amenability, characteristic classes, quasification, rigidity, orbit equivalence.