The main principles of ARGENT, a new software package for multistage reaction design on the basis of the Formal-Logical Approach, are presented. The distinctive features that must make ARGENT a versatile and efficient tool for finding new types of chemical interconversions are discussed. A general outline of the reaction hierarchy within the present state of the Formal-Logical Approach (S.S. Tratch, N.S. Zefirov, J. Chem. Inf. Comput. Sci., 1998, v.38, pp.331-348, 349-366) is given in the first paper of the series, and the relationship of this hierarchy with the structure of the first program implementation (ARGENT-1) is described. The second paper describes the mathematical models (based on the theory of permutation groups) that form the foundations of the generation algorithm in ARGENT-1. Each stage of the generation procedure is based on labeling of vertices and edges of a graph representing the target reactions in a more or less generalized way. To ensure irredundancy of generation, nonequivalent labelings are selected as representatives of orbits of induced permutation groups on the set of all possible labelings. In the third paper of the series, the actual generation algorithm used in ARGENT-1 is described. The generation procedure is based on backtrack traversal of the generation tree, where each node corresponds to assignment of some label to some site (vertex or edge) of a graph representing the reaction in some generalized way. Exclusion of duplicates during generation is achieved via an original and very efficient canonicity testing subprocedure; other ”unsatisfactory” reactions are rejected through the use of so-called preliminary, strong, and weak conditions during generation. The extremely high performance of the suggested algorithm is demonstrated, and the correctness of the results is verified by the example of cyclic bond redistributions.