Diophantine equations are polynomial equations for which integer (or sometimes rational) solutions are sought. The oldest examples date from ancient Greek times, and Diophantus in particular solved many such equations. His methods and the questions they raised inspired much of modern number theory, beginning with the work of Fermat and Euler. Euler, and later Gauss, introduced algebraic integers to solve Diophantine equations, implicitly or explicitly using "unique prime factorization" to do so.

This is a preliminary text introducing the terminology, basic concepts and tools for the next chapters. It reflects six main streams in the area. At the beginning some basic combinatorics related to words is introduced. Then several important classes of words: Fibonacci, Thue-Morse and de Bruijn words. It is followed by a description basic structures for handling texts, like suffix trees, suffix arrays and de Bruijn graphs and by some elements on text compression. The chapter ends with the important issue concerning pseudocodes of algorithms. Their presentation is done in a simple and understandable form since this is a central element of the book.