A Summary of Observed Data and Pre-Amble -- Energy-Density Functional Formalism and Nuclear Masses -- The Decay Process, Fission Barrier, Half-Lives, and Mass Distributions in the Energy-Density-Functional Approach -- Spontaneous Fission Half-Lives of Fermium and Super-Heavy Elements -- Empirical Barrier and Spontaneous Fission -- Induced Fission -- Hot and Cold Fission -- Isomer Fission -- Cluster Radioactivity -- The Relation Between the Asymptotic Kinetic Energy, and the Condition for the Existence of a Meta-Stable State -- The Expression for Half-Lives of Particles Tunneling Through the Barrier Shown in Fig. A. 2 -- Diagonalization of the Coupled Set of Equations Describing Fission.It is the first application to nuclear physics from energy-density functional method, for which Professor Walter Kohn received the Nobel Prize in Chemistry. The book presents a comprehensive extension of the Bohr-Wheeler theory with the present knowledge of nuclear density distribution function.