An antenna with a self-complementary structure has a constant input impedance, independent of the source frequency and of the shape of the structure. The principle for this property of constant impedance was discovered by Professor Mushiake himself. This is the first study which comprehensively describes the principles of self-complementarity in antennas. It explains the theory which was the basis of the development of this principle and presents various engineering applications with an emphasis on extremely broadband self-complementary antennas. Self-Complementary Antennas will be of particular interest to antenna engineers working with extremely large bandwidths and more generally to electrical engineers with an interest in the development of the field since 1948.