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.