The development of the Associative Structure Computer (ASC) was partly motivated by the opportunities and problems of designing, manufacturing, interconnecting and using batch fabricated devices, particularly cryotrons. Some of these points are discussed in the third paper of this series, "The Associative Structure Computer," which describes the machine organization. ASC is constructed with only two types of modules. One module is described in the second paper of this series, "The Associative Switching Structure." This paper, the first of the series, discusses the other module, the Associative Memory Structure.