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We are entering the era of robots, for everyone, everywhere. The expectations of the robots being reliable, intelligent and friendly artificial creatures drive the key challenges of the state-of-the-art robotics: technological, practical and social. The latter is of particular importance, as the extent to which the robots will be accepted in our social environments largely depends on whether they will accommodate the norms of our society. In this thesis, we venture a multidisciplinary effort at the intersection of social studies, economy and robotics. We explore the notion of institution to design social multi-robot behaviors, where institutions allow for interpretation of abstract norms formulated in human language in terms of robot-understandable terminology. In our formalism, institutions are reusable structures that provide abstraction, encapsulation and formalization of generic social norms and allow for governance over miscellaneous robot behaviors and integration of social norms of diverse nature. The core mechanism of our framework -- norm realization, forms the translation layer between the institutional abstraction and a specific system. Norm realization is founded on three key ingredients. First, the representation of norms in a universal form of human language, which introduces a degree of generality necessary to achieve conceptualization, systematization and reusability of norms. Such universal representation is shown to have a high potential to facilitate the integration of existing solutions for diverse applications and social contexts without resorting to the use of heuristics. Second, the development of a clear semantics, necessary for the interpretation of the norms at both abstract and concrete level, and for the implementation of social norms in a plug-and-play manner instead of programming hard-wired social compliance in ad-hoc behaviors. Third, a step-by-step approach for addressing the question of how to apply a generic, language-defined norm into robot terminology, making it readily implementable and executable in physical systems under specific constraints. The proposed formalism embraces low-level sophistication to adopt the complexity of continuous multi-robot behaviors, at the same time retaining the desirable high-level properties. We showcase the power of norm realization through a number of norms encompassing a large variety of social aspects. We carry out a multi-facet validation of our institutional formalism through three extensive case studies, where we address diverse social contexts involving mixed human-robot teams. We target the deployment of multi-robot systems in real human-populated environments, which are cluttered, unpredictable, and highly dynamic. To this end, we develop methods for overcoming the technological shortcomings along three research thrusts. First, we propose an approach to agile formation control, where the shape of the formation adapts locally and gradually to meet the demands of complex indoor environments. Second, we develop a cooperative localization method for achieving robustness of collective navigation in case of communication failures. Third, we adopt existing single-robot social navigation methods to achieve social awareness in the context of multi-robot systems. With these ingredients, our work is pioneering within the scope of human-aware multi-robot navigation in real, human-populated environments.