Relativistic effects, though minor in light atoms, increase rapidly in magnitude as the atomic number increases. For heavy atom species, it becomes necessary to discard the Schrodinger equation in favor of the Dirac equation. Construction of an effective many-body Hamiltonian that accurately accounts for both relativistic and electron correlation effects in many-electron systems is a challenge. It is only in the past 20-25 years that relativistic quantum chemistry has emerged as a field of research in its own right, and it seems certain that relativistic many-electron calculations of molecular properties will assume increasing importance in the years ahead as relativistic quantum chemistry finds a wider range of applications.With the increasing use of relativistic quantum chemical techniques in chemistry, there is an obvious need to provide experts' reviews of the methods and algorithms. This volume aims to disseminate aspects of relativistic many-electron theories and their exciting developments by practitioners. Together, the nine chapters provide an in-depth account of the most important topics of contemporary research in relativistic quantum chemistry, ranging from quasirelativistic effective core potential methods to relativistic coupled cluster theory.