Isometries between C${}^{\ast }$-algebras with finite corank

We give a characterization of linear isometries with finite corank between two arbitrary unital C${}^{\ast }$-algebras in terms of Jordan ${}^{\ast }$-homomorphisms and ``finite-dimensional remainders’'. Also, the corresponding results are given for linear isometries and linear order embeddings between self-adjoint parts of C${}^{\ast }$-algebras. In the finite-dimensional case, we give new examples of linear isometries between matrix algebras.