This volume contains the proceedings of the NATO Advanced Research Workshop on Numerical Integration that took place in Bergen, Norway, in June 1991. It includes papers for all invited talks and a selection of contributed talks. The papers are organized into four parts: numerical integration rules, numerical integration error analysis, numerical integration applications and numerical integration algorithms and software; many papers are relevant to more than one category. The workshop studied the state of the art in numerical integration (both single and multidimensional). The book contains a number of survey papers by experts on themes such as: numerical solution of integral equations, cubature formulae construction, handling singularities in finite elements, statistical applications, lattice rules, error estimates, error bounds and software.