Quantum Flux Parametron(QFP) is a Josephson junction device which uses the polarities of a unit of quantum flux to represent a bit of binary information. The low power consumption and the inductive nature of signal transfer of QFP promise the realizability of a highly integrated Josephson Supercomputer. The miniaturization and the inductively connected circuits pose new challenges and problems to the designers of such a computer system. This volume contains five papers which provide detailed illustrations of the essential problems in the design of Josephson Supercomputers.The problems include (i) the three-dimensional packaging problems in the highly integrated system, (ii) the detection of trapped magnetic quanta, (iii) the computation of three-dimensional inductance and (iv) the elimination or alleviation of various internal and external operational problems of QFP arising from the limitation of the current fabrication technology as well as the inherent problems of direct coupling of QFP