Building on IMT established expertise in network theory, state-of-the-art as well as advanced methods for network analysis are applied in a twofold way: 1) to identify early-warning signals of upcoming ecological, economic and financial instabilities by employing statistically-grounded benchmark models; 2) to study both the static and the dynamical resilience of a network by exploring its “redundancy”, i.e. the space of network states that are still compatible with the constraints characterizing each node while being less prone to failures. To tackle the first point, a number of quantities describing the structural vulnerability of a system have beeing identified; this same set of indices will, then, be monitored as candidate early-warning indicators. The second problem is approached by exploring the set of “microscopic”, alternative network configurations that preserve certain properties of each node; the viable configurations will, then, undergo static and dynamical stress-tests in order to suggest policy measures to keep the network within the “robust” variants of its original structure. The analysis of the dynamical resilience of a network are carried out by studying how shocks propagate on a given networked structure and on the set of configurations compatible with the same constraints but having a higher resilience. A key framework is that of information theory, which naturally leads to tools for the analysis and inference of complex networks conforming to the maximum-entropy principle: such a framework allows one to preserve part of the empirical network topology while randomizing everything else. Over the years, these methodologies have found three main areas of application: 1) the detection of statistically-significant patterns (i.e. structural properties which are not compatible with a given, reference model); 2) the reconstruction of networked structures from partial information; 3) the enumeration of graphs characterized by a given set of topological properties to preserve. Remarkably, maximum-entropy methods for reconstructing economic and financial networks have been recently found to outperform the competing, probabilistic algorithms by various independent studies and comparisons. With regards to sustainability science, IMT developed innovative methodologies to help Italian municipalities and other decision makers to design policies and strategies for the urban sustainability and the improvement of the environmental performance with respect to digitalization, energy, water, waste management and pollution. A key part of the IMT effort is devoted to increase the citizens sustainability awareness. The production and usage of Open data is encouraged to create “maps of the greenery” throughout the Italian territory. Additionally, IMT is also focusing on the analysis of human mobility by using mobile-phone traces, vehicular GPS and social media data - i.e. proxies of individual as well as collective behavior. In the field of renewable energy sources, the IMT research team is developing a method for the optimal distribution of renewable energy sources at the territorial level, by considering the local energy demand and the historical records concerning the availability of wind and solar energy.