When system runs are modeled with interval orders, interval order structures are useful tools to model abstract concurrent histories, i.e. sets of equivalent system runs. For the general cases, Mazurkiewicz traces allow a representation of the entire partial order by a single sequence with independency relations, and Comtraces allow a representation of stratified order structures by single step sequences with appropriate simultaneity and serializability relations. Unfortunately, both of them are unable to clearly describe the abstract interval order semantics of inhibitor nets. The goal of the thesis is to provide a monoid based model called Interval Traces that would allow a single sequence of beginnings and endings to represent the entire stratified order structures as well as all equivalent interval order observations. And the thesis will also show how interval order structures can be modelled by interval traces and how interval traces can be used to describe interval order semantics. / Thesis / Doctor of Philosophy (PhD)