Professor Grant first became aware of the need to develop a relativistic theory of atomic and molecular structure some 50 years ago in connection with X-ray absorption by heavy metals. In a 1961 paper, he showed that the Dirac-Hartree-Fock equations for atoms could be written in a simple form which has been used in all subsequent atomic calculations. This early work was generalized to permit more accurate multi-configurational calculations in the next two decades, implemented in the widely used GRASP code for relativistic modeling of electronic wavefunctions, energy levels and radiative transition probabilities of spectral lines. The DARC code, an extension of GRASP which is designed to calculate cross sections for atom/ion collisions with low-energy electrons or photons, was developed mainly in the 1980s and is now becoming more relevant for applications involving target atoms of higher atomic number. The BERTHA code is the first relativistic molecular structure code designed to take advantage of the internal structure of Dirac four-component spinors; its speed and accuracy are now beginning to be appreciated and utilized effectively by quantum chemists. The book is designed for all those who would like to know more about the mathematics and physics of relativistic atomic and molecular theory and who wish to use the computational machinery now available to solve problems in atomic and molecular physics and their applications. Professor Grant was elected a Fellow of the Royal Society of London in 1992.