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Now-a-days most of the physical problems involve numerical computation of higher precision. Therefore our intention of preparing this book lies in producing new quadrature rules of higher precision, mixing two or more rules of lower precision. Many quadrature rules like Newton-Cotes type rules and Gaussian rules are available in literature. These are useful to integrate numerically the functions of real and complex variables. Newton-Cotes types of rules are widely used in hard computations for its rational weights and nodes. However it is well known that Gaussian types of rules are more accurate than Newton-Cotes type of rules. Further the approximation obtained by applying a single quadrature rule on an integral (whose value is otherwise unknown) can't be reliable. But approximating the same integral by two rules of same precision and a mixed quadrature rule obtained by these former can be ascertained up to some extent. Keeping the above facts in mind, in this book I have developed some mixed quadrature rules.