The authors examine in detail the fundamentals and mathematical descriptions of the dynamics of automobiles. In this context, different levels of complexity are presented, starting with basic single-track models up to complex three-dimensional multi-body models. A particular focus is on the process of establishing mathematical models based on real cars and the validation of simulation results. The methods presented are explained in detail by means of selected application scenarios. In addition to some corrections, further application examples for standard driving maneuvers have been added for the present second edition. To take account of the increased use of driving simulators, both in research, and in industrial applications, a new section on the conception, implementation and application of driving simulators has been added.