This Book (White Paper) 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: I. IDEOLOGY & STRATEGY of the ASI Project II. THEORY & METHODOLOGY of ASI Development III. CONCEPTUAL MODEL of ASI System IV. PRE-PROJECT R&D Task Setting V. CONCLUSION & DISCUSSION, incl. AI Safety (A) APPENDICES with reviews of relevant scientific and R&D areas, incl. frontier AI Models The Book may be useful and interesting for the staff of organizations & 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 & officials. Of course - all intellectual, educated and ethical people with progressive worldviews, interested or anyway considered in above presented problematics. This version 4 (16) with 2024 UPDATE — new Chapters and Appendices