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Immune responses in metazoans involve hierarchical kinetic non-linear processes across multiple length and time scales from interaction between molecules to coordinated movements of immune cells in lymph nodes. Therefore, combining mathematical techniques designed to examine such complex systems with wet lab experiments is a necessary step to decipher mechanisms as well as to gain systems level understanding into the immune system. We use mathematical techniques based on statistical physics, engineering, and nonlinear dynamics in synergistic collaboration with our experimental colleagues to understand responses in innate and adaptive immune system. The focus of our current research are knowing, (i) how Natural Killer (NK) cells, an important player of our innate immunity providing resistance against viral infections and tumors, mount decisive (activation or tolerance) in response to diverse stimuli, (ii) the mechanisms underlying the interaction of membrane lipid metabolism with receptor signaling in shaping the T cell (a key orchestrator of our adaptive immunity) repertoire in mammals, (iii) the key regulators of the homeostatic relationship between the host immune system and the resident microbiota in the metazoan gut and the upper respiratory tract.