The science of systems requires a specific and constructive mathematical model and language which would describe jointly such systemic categories as adaptation, self-organization, complexity, and bring the applied tools for building a system model for each specific object of a diverse nature. This formalism should be connected directly with a world of information and computer applications of a systemic model, developed for a particular object. The aim of the considered information systems theory (IST) is to build a bridge between the mathematical systemic formalism and information technologies. The objective is to develop a constructive systemic model of revealing information regularities and specific information code for each object. To fulfill the goal and the considered systems' definition, the IST joins two main concepts. First is the unified information description of the different nature's interacted flows, with a common information language and systems modeling methodology, applied to distinct interdisciplinary objects. Second is the general system's information formalism for building the model, which allows expressing mathematically the system's regularities and main systemic mechanisms. This formalism is represented by informational macrodynamics (IMDs), which reveals the system model's main layers: microlevel stochastics, macrolevel dynamics, hierarchical dynamic network (IN) of information structures, its minimal logic, and optimal code of communication language, generated by the IN hierarchy, dynamics, and geometry. The system's complex dynamics originate information geometry and evolution with the functional information mechanisms of ordering, cooperation, mutation, stability, diversity, adaptation, self-organization, and the double helix's genetic code. The developed IMD's theoretical computer-based methodology and software has been applied to such areas as technology, communications, computer science, intelligent processes, biology, economy, m- anagement, and other nonphysical and physical subjects. The review is written for a broad reader's audience familiar with basic physics, calculus, and computers.