This paper develops nonsmooth Lyapunov stability theory and LaSalle's invariance principle for systems with nonsmooth dynamics, specifically those described by Lipschitz continuous Lyapunov functions and absolutely continuous state trajectories. The authors derive computable tests based on Filipov's differential inclusion and Clarke's generalized gradient. These results are particularly useful for analyzing the stability of equilibria in differential equations with discontinuous right-hand sides, such as in nonsmooth dynamic systems or variable structure control. The paper introduces a new chain rule for differentiating regular functions along Filipov solution trajectories, which is essential for computing the generalized gradient of nonsmooth Lyapunov functions. Two stability theorems are presented: uniform stability and uniform asymptotic stability, both stated in terms of the set-valued map \(\hat{V}\). The paper also provides an example to illustrate the application of these theorems to a spring-mass-Coulomb friction system, demonstrating that the equilibrium cannot be proven stable using smooth Lyapunov functions. Finally, a nonsmooth version of LaSalle's theorem is proved, showing that trajectories in a compact set converge to the largest invariant set in the closure of the set where the Lyapunov function is zero.This paper develops nonsmooth Lyapunov stability theory and LaSalle's invariance principle for systems with nonsmooth dynamics, specifically those described by Lipschitz continuous Lyapunov functions and absolutely continuous state trajectories. The authors derive computable tests based on Filipov's differential inclusion and Clarke's generalized gradient. These results are particularly useful for analyzing the stability of equilibria in differential equations with discontinuous right-hand sides, such as in nonsmooth dynamic systems or variable structure control. The paper introduces a new chain rule for differentiating regular functions along Filipov solution trajectories, which is essential for computing the generalized gradient of nonsmooth Lyapunov functions. Two stability theorems are presented: uniform stability and uniform asymptotic stability, both stated in terms of the set-valued map \(\hat{V}\). The paper also provides an example to illustrate the application of these theorems to a spring-mass-Coulomb friction system, demonstrating that the equilibrium cannot be proven stable using smooth Lyapunov functions. Finally, a nonsmooth version of LaSalle's theorem is proved, showing that trajectories in a compact set converge to the largest invariant set in the closure of the set where the Lyapunov function is zero.