The subject of research of the dissertation is directed regular graphs constructed from transitive permutation groups. In the first part of the dissertation, the notions and facts of group theory, design theory, graph theory, and coding theory are introduced. In the second part of the thesis the properties of directed quasi-strongly regular graphs are analyzed and the methods for their construction from the adjacency matrices of known directed quasi-strongly regular graphs are introduced and proved. Moreover, the existing method for constructing 1-designs from transitive permutation groups is described and modified for the purpose of constructing directed regular graphs. Also, an analysis of the possibility of using the construction with the aim of constructing directed regular graphs with the assumed non transitive action of the finite group is presented. In the third chapter, the algorithm of the modified method for constructing directed regular graphs using stabilizer orbits for the action of the transitive permutation group on the finite set is described. The above is supported by concrete examples and complete or partial classifications of (directed) strongly regular and quasi-strongly regular graphs. In the last chapter, self-orthogonal and LCD codes are constructed from adjacency matrices of directed strongly regular graphs and their properties are analyzed. The program package GAP ([32]) and its packages DIGRAPHS ([24]) and GUAVA ([28]) as well as the program package MAGMA ([6]) are used for all the above constructions.