This book summarizes the enormous amount of material accumulated in the field of nuclear density functional theory over the last few decades. The goal of the theory is to provide a complete quantum-mechanical description and explanation of nuclear phenomena in terms of the local density distribution as a basic ingredient rather than the many-particle wavefunction. This leads to a considerable reduction in the mathematical complexity of nuclear many-body problems and to a great conceptual simplicity and visual clarity in its theoretical treatment.The authors develop the mathematical framework on which the theory is based and consider the associated approaches used to analyse experimental data in a variety of nuclei and nuclear processes with widely differing properties.