The object of our research is the codification of programming knowledge for the synthesis of concurrent programs. This is important because concurrency is a way of securing better performance on amenable problems than is available on non-concurrent computers. We divide this knowledge into two sections: knowledge for the synthesis of arrays of processors that could be connected in a geometrically regular manner (crystalline concurrency), and knowledge for the synthesis of tree structure (tree concurrency). We divide synthesis of crystalline concurrency, in turn into several subsections: synthesis of declarations of multiple processors and the wires implied by the dependencies among the values they contain reduction of this wire network to a smaller wire network creation of subnetworks to replace an overly-broad fanout network, virtualization which is the creation of additional array elements and processors to reflect the internal enumerations that comprise the computation of a datum and aggregation which is the merging of several processors into one. We use a transformational approach. The transformational system has rules each of which contains two predicates: an antecendent and a consequent. If the antecedent of a rule is true of a given object, the rule applies and the object is modified to make the consequent true. (Author)