A family of Fredholm operators has an invariant called the index which takes values in the K-group of the space of parameters. My talk is devoted to Fredholm realizations of semi-Fredholm operators in a Hilbert space. Such a realization is determined by an abstract boundary condition, which is a subspace of the space of abstract boundary values. I find the index of a family of Fredholm realizations in terms of the corresponding family of boundary conditions. I also prove a similar result for self-adjoint Fredholm extensions of symmetric semi-Fredholm operators.