This is a book about algorithms for performing arithmetic, and their implementation on modern computers. We are concerned with software more than hardware – we do not cover computer architecture or the design of computer hardware since good books are already available on these topics. Instead, we focus on algorithms for efficiently performing arithmetic operations such as addition, multiplication, and division, and their connections to topics such as modular arithmetic, greatest common divisors, the fast Fourier transform (FFT), and the computation of special functions. The algorithms that we present are mainly intended for arbitrary-precision arithmetic. That is, they are not limited by the computer wordsize of 32 or 64 bits, only by the memory and time available for the computation. We consider both integer and real (floating-point) computations.