The nature of C ]*-algebras is such that one cannot study perturbation without also studying the theory of lifting and the theory of extenstions. Approximation questions involving representations of relations in matrices and C ]*-algebras are the central focus of this volume. A variety of approximation techniques are unified by translating them into lifting problems: from classical questions about transivity of algebras of operators on Hilbert spaces to recent results in linear algebra. One chapter is devoted to Lin's theorem on approximating almost normal matrices by normal matrices. The...