This work aims to develop a driving risk warning system to enhance the road safety. Different from the existing lane departure warning system, speed limit warning system or collision warning system, the warning system proposed in this work focuses on the safety regarding vehicle's dynamics states. Many road accidents are caused by losing control of vehicle dynamics, such as the rollover, car drift and brake failure. First of all, the importance of monitoring vehicle dynamics states, especially the tire forces, is explained. Then the driving risk assessment criteria based on tire forces are developed in this work. The main contribution of this paper is the development of vehicle dynamics models and observers to estimate and predict individual tire forces using only low-cost sensors and ADAS (Advanced Driver Assistance Systems) map. The major new techniques developed in this study can be summarized in three aspects: (1) development of new vehicle dynamics models to estimate vertical, longitudinal, and lateral tire forces, (2) development of new nonlinear observers to minimize the estimation errors caused by sensor noises and model uncertainty, and (3) development of the tire forces prediction algorithm by taking advantage of digital map. The proposed warning system is validated by real vehicle experiments.