This paper introduces a unified approach to robustness analysis with respect to nonlinearities, time variations, and uncertain parameters. The approach is based on integral quadratic constraints (IQC's), which allow the description of complex systems using elementary components. A stability theorem for systems described by IQC's is presented, covering classical passivity/dissipativity arguments but simplifying the use of multipliers and the treatment of causality. The paper also discusses a systematic computational approach and relates IQC's to other methods of stability analysis. A summarizing list of IQC's for important types of system components is provided. The paper begins by discussing the importance of using simple models in control system design and the need for formal analysis of systems. It then reviews the development of absolute stability theory in the 1960s and 1970s, highlighting the use of multipliers and the limitations of causality conditions. Recent advances in computation, such as algorithms for structured singular values and polynomial time algorithms for convex optimization, have enabled more accurate robustness analysis. The paper then presents a basic stability theorem for systems described by IQC's, showing that multipliers can be introduced without causality constraints. This makes the theory more accessible and enhances the development of computer tools for stability analysis. The paper discusses the use of IQC's to describe relationships between signals in a system component, with examples such as saturation and delay. The paper also addresses the use of IQC's in robustness analysis, including the application of IQC's to systems with saturation and delay. It discusses the use of IQC's for uncertain time delay and provides a list of IQC's for various types of system components, including uncertain linear time-invariant dynamics, constant real scalar, time-varying real scalar, coefficients from a polytope, periodic real scalar, multiplication by a harmonic oscillation, slowly time-varying real scalar, and delay. The paper concludes with a discussion of the relationship between IQC's and quadratic stability, showing that they are equivalent in certain cases.This paper introduces a unified approach to robustness analysis with respect to nonlinearities, time variations, and uncertain parameters. The approach is based on integral quadratic constraints (IQC's), which allow the description of complex systems using elementary components. A stability theorem for systems described by IQC's is presented, covering classical passivity/dissipativity arguments but simplifying the use of multipliers and the treatment of causality. The paper also discusses a systematic computational approach and relates IQC's to other methods of stability analysis. A summarizing list of IQC's for important types of system components is provided. The paper begins by discussing the importance of using simple models in control system design and the need for formal analysis of systems. It then reviews the development of absolute stability theory in the 1960s and 1970s, highlighting the use of multipliers and the limitations of causality conditions. Recent advances in computation, such as algorithms for structured singular values and polynomial time algorithms for convex optimization, have enabled more accurate robustness analysis. The paper then presents a basic stability theorem for systems described by IQC's, showing that multipliers can be introduced without causality constraints. This makes the theory more accessible and enhances the development of computer tools for stability analysis. The paper discusses the use of IQC's to describe relationships between signals in a system component, with examples such as saturation and delay. The paper also addresses the use of IQC's in robustness analysis, including the application of IQC's to systems with saturation and delay. It discusses the use of IQC's for uncertain time delay and provides a list of IQC's for various types of system components, including uncertain linear time-invariant dynamics, constant real scalar, time-varying real scalar, coefficients from a polytope, periodic real scalar, multiplication by a harmonic oscillation, slowly time-varying real scalar, and delay. The paper concludes with a discussion of the relationship between IQC's and quadratic stability, showing that they are equivalent in certain cases.