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This book is designed as an advanced guide to numerical methods applied in science. It covers the following topics of practical numerical methods: solution of systems of equations: Gauss, Gauss-Jordan, Cramer, Inverse Matrix, Jacobi, Gauss-Seidel, Gauss-Seidel with relaxation, the least squares method for a polynomial fit (regression analysis), elliptic covariance, the least squares method in connection with maximum likelihood, elliptic covariance and the determination of the energy calibration equation (K ), Moseley's law. It is included the derivation of many formulas to clarify the concepts of numerical methods applied in science. It is hoped that this book will cover all the needs of the students to understand the fundamentals of numerical methods and will achieve the interest and motivation of the students for this topic.