The foundations of system analysis as an applied scientific methodology assigned for the investigation of complex and highly interdisciplinary problems are provided in this monograph. The basic definitions and the methodological and theoretical basis of formalization and solution processes in various subject domains are presented. The methods of formalizing the system tasks and reducing them to a solvable form under real-world conditions and by taking into account e.g. sets of contradictory purposes, quantitative and qualitative characteristics of information, different kinds of uncertainties and risks are described in detail. In addition, the authors propose methods for disclosing the conceptual uncertainty and develop a strategy for system interaction and counteraction of coalitions under multi-factorial risks. All these topics are supported by the presentation of computing algorithms and solution procedures for practical problems in socio-economics and in technology, e.g. for designing complex interconnected systems to function under the conditions of uncertainties and risks. This monograph will be useful for researchers, post-graduates and advanced students specializing in system analysis, decision making, strategic planning or engineering design.