Input-to-state stability (ISS) is a concept used to analyze the stability of nonlinear input/output (i/o) systems. This paper discusses the basic concepts and results of ISS, focusing on the formulation of robustness with respect to disturbances. The paper emphasizes the importance of understanding how system responses are affected by external signals and how to unify state-space and input/output stability theories. The main goal is to develop a set of concepts for studying systems through decomposition, quantify system responses to external signals, and unify different stability theories. The paper defines ISS as a notion of stability for i/o systems, where the system's output depends on its input. The idea is to formalize the concept of stability for the mapping from input to output. The paper discusses desirable properties of such systems, including how bounded, eventually small, integrally small, or convergent inputs produce outputs with the same properties. It also considers the impact of initial states and transients on system behavior. The paper highlights the importance of ISS in control theory, particularly in the context of feedback systems. It provides an overview of the key concepts and results related to ISS, including the relationship between theoretical concepts and constructive control methods. The paper also references previous work and surveys, and provides some pointers to the literature for applications and extensions of the basic framework. However, it does not focus on specific feedback design or engineering problems, referring the reader to other textbooks for more detailed information.Input-to-state stability (ISS) is a concept used to analyze the stability of nonlinear input/output (i/o) systems. This paper discusses the basic concepts and results of ISS, focusing on the formulation of robustness with respect to disturbances. The paper emphasizes the importance of understanding how system responses are affected by external signals and how to unify state-space and input/output stability theories. The main goal is to develop a set of concepts for studying systems through decomposition, quantify system responses to external signals, and unify different stability theories. The paper defines ISS as a notion of stability for i/o systems, where the system's output depends on its input. The idea is to formalize the concept of stability for the mapping from input to output. The paper discusses desirable properties of such systems, including how bounded, eventually small, integrally small, or convergent inputs produce outputs with the same properties. It also considers the impact of initial states and transients on system behavior. The paper highlights the importance of ISS in control theory, particularly in the context of feedback systems. It provides an overview of the key concepts and results related to ISS, including the relationship between theoretical concepts and constructive control methods. The paper also references previous work and surveys, and provides some pointers to the literature for applications and extensions of the basic framework. However, it does not focus on specific feedback design or engineering problems, referring the reader to other textbooks for more detailed information.