This book is designed as an advanced guide for numerical methods in the science. It covers many topics of practical numerical methods applied in the science: solutions of equations with one variable: bisection, secant, false rule, Newton-Raphson, fixed point, etc., solution of systems of equations: Gauss, Gauss-Jordan, Cramer, Inverse Matrix, Jacobi, Gauss-Seidel, Gauss-Seidel with relaxation, etc., polynomial interpolation: Lagrange interpolation, Newton interpolation, interpolation with equidistant spaces, etc., the method of the least square method for a polynomial fit (regression analysis), etc., numerical derivatives, finite differential discretization of the derivative, numerical integrations: trapeze method, Simpson 1/3, Simpson 3/8, differential equations: Euler, Runge-Kutta, differential equations with boundary values, etc. It is included the deduction of many formulas in order to clear the concepts of the numerical methods applied in Science. It is hoped that this book fills all needs of the students to get the fundaments of the numerical methods and to achieve the interest and motivation of the students for this topic.