Affine linking numbers, their applications, and operations on generalized strings". based on joint works with Yuli Rudyak. Abstract: The linking number $lk$ is a classical invariant of two zero homologous submanifolds $N_1$ and $N_2$ of $M$, such that $dim N_1+dim N_2+1=dim M$. Homology theory definition of linking numbers works only when $N_1$ and $N_2$ are zero homologous or are elements of finite order. We use the homotopy theory interpretation of the linking number to construct the "affine linking number" generalization of $lk$ to all nonzero homologous submanifolds of an arbitrary $M$. When linking number $lk$ is defined affine linking number often appear to be a splitting of $lk$ into a collection of independent invariants. The construction of affine linking numbers is based on a new operation on Bordism groups of the spaces of mappings $N_1\to M$ and $N_2\to M$. This operation is the natural generalization of Chas-Sullivan string homology Lie bracket on $H_*((Maps S^1\to M)/SO(2))$ to the case of bordism groups of maps of mappings of arbitrary $P\to M$. We generalize other operations of string homology using similar ideas. We apply affine linking numbers to the study of causality of events and show that they often allow to detect that two events are causally related. This can be done from the pictures of the fronts of the events at some time moment without the knowledge of the time-dependent fronts propagation law and of the times and places of the events.