This volume describes techniques of computation and approximation that may be used to mentally and rapidly calculate mathematical quantities, including results of arithmetic operations and values of elementary functions. These methods range from very old to recent to brand new. They are not shortcuts, rather, the book is aimed at sharpening the mental skills needed to perform "mathematical acrobatics". The book is intended for those whose interest in mathematics has engendered a general appreciation of numbers and a desire to expand their capacities of abstract thought. It presents a set of useful and challenging methods and algorithms for quick mental computation of products, quotients, roots of non-perfect powers, and trigonometric, logarithmic and exponential values. Chapters begin with quotes from mathematicians and philosophers, such as Bertrand Russell, James Lowell and Alfred North Whitehead.