This monograph is dedicated to a novel approach for uniform modeling of timed and hybrid systems. The author introduces a time model that allows for both the description of discrete time steps and continuous processes with a discrete time model with infinitesimal step widths.

The underlying mathematical structure of this time model is based on the concepts of non-standard analysis. The discrete modeling, i.e., the description of sequential discrete algorithms at different abstraction levels, is done using the abstract state machines formalism.

The presentation is well balanced between theoretical elaboration and critical discussion of the applicability of the theoretical results by means of appropriate case studies. The new temporal semantics proposed helps theoreticians as well as practitioners in gaining a better understanding of time models and in building better notations, models, and tools for the formal treatment of systems where time matters.