This Book proposes a Project Conception of Artificial Super Intelligence ASI, based on (strong) system approach and wide theoretical-methodological framework – Cybernetics, Synergetics, Semiotics, Mathematics, Cognitology and Artificial Intelligence. Contents:•IDEOLOGY and STRATEGY of the ASI Project•THEORY and METHODOLOGY of ASI Development•CONCEPTUAL MODEL of ASI System•PRE-PROJECT R&D Task Setting•CONCLUSION and DISCUSSION, incl. AI Safety•APPENDICES with reviews of relevant scientific and R&D areas, incl. frontier AI ModelsThe Book may be useful and interesting for the staff of organizations and enterprises concerned with AI R&D and implementations in different areas, firstly – perspective AGI/ASI systems. In addition – for Customers, Investors and Sponsors of such R&Ds, private, public and states – its owners and officials. Of course - all intellectual, educated and ethical people with progressive worldviews, interested or anyway considered in above presented problematics.