Abstract: We shall explain what it means for a group to be negatively curved (according to Gromov). Basic examples include free groups and fundamental groups of closed manifolds with negative (sectional) curvature. In a more general sense, amalgamated products of groups have negative curvature. Then we will present an algebraic (cohomological) way to capture these notions. We introduce an invariant that allows to prove general rigidity results in geometry and dynamics. This talk will be completely introductory and no previous knowledge will be assumed.