The notion of time plays an important role in modern science. In computer science and artificial intelligence, the parameter of time is of particular importance, e.g. for planning robot activity, natural language processing, and time-varying scene analysis. This work investigates the relationship between classic, first-order theories of point- and interval-based time structures, modal logics of corresponding structures, and their algorithmic representations. To make this relationship complete, a formalisation of Allen's famous algorithm, applicable to various structures of time, is presented along with its translation to modal logics. All in all, the book is a competent and comprehensive analysis of logical descriptions and algorithmic representations of time structures.