A research program is present on advanced methodologies for water resources planning. It summarizes the various achievements accomplished during the period of the project. The main portion of the project is devoted to the presentation of a working manual for use by practicing water resources engineers and analysts, showing the application of the discrete differential dynamic programming (DDDP). The brief theoretical background of the DDDP methodology and a review of the principal aspects of its theory are included. Then, a detailed description of the DDDP methodology is given, giving emphasis to the key steps of its procedure. The DDP methodology as a means to solve already formulated dynamic programming problems is proposed. For illustrative purposes, three examples are given to show the application of the DDDP methodology in the solution of optimization problems arising from the planning and operation of the complex water resources projects. (Modified author abstract)