Abstract: Based on the author’s personal research experience, this paper introduces the theory and applications of antenna optimization design, with content covering the general theory of antennas, single-antenna design and array-antenna synthesis. The stored energies in medium and the stored energies of antenna as well as the upper bounds of the gain-bandwidth product are first introduced, thereby providing theoretical basis and guidelines for antenna design. Second, two fundamental theories of single-antenna design are expounded, including the resonant mode theory which is based on the stored energies of antenna, and the thin wire model theory for the analysis of radiation characteristics of metallic antennas. Finally, the method of maximum power transmission efficiency for array-antenna synthesis is elaborated, covering the unconstrained, weighted, and constrained formulations and their applications in the wireless power transmission and pattern synthesis.