Continued fractions were studied by the great mathematicians of the seventeenth and eighteenth centuries and are a subject of active investigation today. Fractions of this form provide much insight into many mathematical problems, particularly into the nature of numbers, and the theory of continued fractions is a powerful tool in number theory and other mathematical disciplines. The author of this book presents an easy-going discussion of simple continued fractions, beginning with an account of how rational fractions can be expanded into continued fractions. Gradually the reader is introduced to such topics as the application of continued fractions to the solution of Diophantine equations, and the expansion of irrational numbers into infinite continued fractions.