Ecological (eco)-driving aims at improving fuel economy of a vehicle by taking smooth driving action in the road traffic networks. This tutorial paper presents an advanced eco-driving system for a host vehicle that uses information of surrounding vehicles, road gradients and the state of upcoming traffic signal to predict the future traffic states using the dynamical models, and based on the predicted information it generates the optimal vehicle control inputs in a model predictive control framework. The control objective is considered to maximize fuel economy by regulating a safe headway distance or cruising at the optimal velocity under bounded driving torque condition. A fast optimization technique using continuation and generalized minimum residual (C/GMRES) method is used in the framework for real-time optimization of control inputs. The proposed eco-driving system is evaluated in highly interactive urban traffic using the microscopic traffic simulator Aimsun, and its performance is compared with the traditional driving system.