This book is an intellectually stimulating excursion into mathematical machines and structures capable for a universal computation. World top experts in computer science and mathematics overview exciting and intriguing topics of logical theory of monoids, geometry of Gauss word, philosophy of mathematics in computer science, asynchronous and parallel P-systems, decidability in cellular automata, splicing systems, reversible Turing machines, information flows in two-way finite automata, prime generators in automaton arrays, Grossone and Turing machines, automaton models of atomic lattices. The book is  full of visually attractive examples of mathematical machines, open problems and challenges for future research. Those interested in the advancement of a theory of computation, philosophy of mathematics, future and emergent computing paradigms, architectures and implementations will find the book vital for their research and development.

The common structure of the curves having a same Gauss word.- Logical theory of the additive monoid of subsets of natural integers.- Some reflections on mathematics and its relation to computer Science.- Sampling a Two-way Finite Automaton.- Constructing reversible Turing machines by reversible logic element with memory.- The Grossone methodology perspective on Turing machines.- On Parallel Array P Systems.- Computational models based on splicing.- Linear Cellular Automata and Decidability.- Algorithms with Active Cells Modeled by Cellular Automata with Write-Access (CA-w).- Broadcasting automata and patterns on Z2.- Real-Time Prime Generators Implemented on Small-State Cellular Automata.- Phyllosilicate Automata.