One of the most remarkable features of the human brain is its ability to adapt rapidly and efficiently to external task demands. Novel and non-routine tasks, for example, are implemented faster than structural connections can be formed. The neural underpinnings of these dynamics are far from understood. Here we develop and apply novel methods in network science to quantify how patterns of functional connectivity between brain regions reconfigure as human subjects perform 64 different tasks. By applying dynamic community detection algorithms, we identify groups of brain regions that form putative functional communities, and we uncover changes in these groups across the 64-task battery. We summarize these reconfiguration patterns by quantifying the probability that two brain regions engage in the same network community (or putative functional module) across tasks. These tools enable us to demonstrate that classically defined cognitive systems-including visual, sensorimotor, auditory, default mode, fronto-parietal, cingulo-opercular and salience systems-engage dynamically in cohesive network communities across tasks. We define the network role that a cognitive system plays in these dynamics along the following two dimensions: (i) stability vs. flexibility and (ii) connected vs. isolated. The role of each system is therefore summarized by how stably that system is recruited over the 64 tasks, and how consistently that system interacts with other systems. Using this cartography, classically defined cognitive systems can be categorized as ephemeral integrators, stable loners, and anything in between. Our results provide a new conceptual framework for understanding the dynamic integration and recruitment of cognitive systems in enabling behavioral adaptability across both task and rest conditions. This work has important implications for understanding cognitive network reconfiguration during different task sets and its relationship to cognitive effort, individual variation in cognitive performance, and fatigue. 