Preliminaries -- Perturbations of Linear Systems -- Linear Systems with Slowly Varying Coefficients -- Linear Dissipative and Piecewise Constant Systems -- Nonlinear Systems with Autonomous Linear Parts -- The Aizerman Problem -- Nonlinear Systems with Time-Variant Linear Parts -- Essentially Nonlinear Systems -- The Lur'e Type Systems -- The Aizerman Type Problem for Nonautonomous Systems -- Input - State Stability -- Orbital Stability and Forced Oscillations -- Positive and Nontrivial Steady States.Explicit Stability Conditions for Continuous Systems deals with non-autonomous linear and nonlinear continuous finite dimensional systems. Explicit conditions for the asymptotic, absolute, input-to-state and orbital stabilities are discussed. This monograph provides new tools for specialists in control system theory and stability theory of ordinary differential equations, with a special emphasis on the Aizerman problem. A systematic exposition of the approach to stability analysis based on estimates for matrix-valued functions is suggested and various classes of systems are investigated from a unified viewpoint.