The terms “information space” and “cyberspace” form the basis of definitions of information security and cyber security. The actual issue is to determine the essence of the phenomena of the information and cyberspace, which currently do not have a unified vision. The paper proposes a study of the structure and properties of the information space and cyber space, based on a mathematical formalism, which distinguishes the work from the previous ones, where the corresponding spaces were considered descriptively. The information and cyberspaces are considered as complex systems to which a system approach is applied. Structural models of information and cyberspaces consisting of subsystems of the first, second, and third levels, and elements of the fourth level are offered. Based on the proposed models of systems, the indicators of integrity and autonomy are analyzed, which allows us to conclude that, in both spaces, there is a greater tendency to the structural monolithicity than to the autonomy of the components. But cyberspace shows a greater interdependence of components, compared to the information space, despite their higher dynamism and a less degree of attachment to real objects. The Jacquard similarity coefficient is calculated for the elements of the 4th level. It indicates a significant difference between the systems of the information space and the cyberspace. Descriptive analysis of the elements of the information and cyberspaces showed that the cyberspace, in contrast to the information space, operates not only information, but also data that are necessary to support its technological functioning. Another distinctive feature of the cyberspace is the information control to achieve a specific goal; while the information space deals only with the processing and storage of information.