This book presents numerical methods for solving a wide range of problems associated with the structure of atoms and simplest molecules, and their interaction with electromagnetic radiation, electrons, and other particles. It introduces the ATOM-M software package, presenting a unified software suite, written in Fortran, for carrying out precise atomic and molecular numeric calculations. The book shows how to apply these numerical methods to obtain many different characteristics of atoms, molecules, and the various processes within which they interact. In an entirely self-sufficient approach, it teaches the reader how to use the codes provided to build atomic and molecular systems from the ground up and obtain the resulting one-electron wave functions. The computational programs presented and made available in this book allow calculations in the one-electron Hartree-Fock approximation and take into account many-electron correlations within the framework of the random-phase approximation with exchange or many-body perturbation theory. Ideal for scholars interested in numerical computation of atomic and molecular processes, the material presented in this book is useful to both experts and novices, theorists, and experimentalists.