Despite the numerous experimental investigations performed over the past century and more intensively in the last fifteen years, strain-induced crystallization in natural rubber still remains hardly understood in its precise mechanisms: a complete theoretical description for crystallization and melting of the involved crystallites is still needed to derive relevant physically-based mechanical constitutive equations. Therefore, the present Part I of our work proposes a coherent theory describing the full nucleation–growth–melting cycle of these crystallites, by using classical thermodynamics of phase transitions and by accounting for the topological constraints due to the network. A graphical representation of crystallite evolution involving strain, temperature, and crystallite size is then introduced, using a physical parameter to express the change of Gibbs free energy due to surface creation for a unit volume of crystalline phase. Finally, experimental results from literature exhibiting shape-memory effects in rubber are elucidated using this crystallite life cycle theory.