This report describes the Variable Metric Method for minimizing differentiable functions of several variables. The method determines a matrix that characterizes the function's behavior near a minimum. For quadratic functions, no more than N iterations are needed, where N is the number of variables. The method allows for linear constraints on variables without altering the procedure. The method is based on geometric concepts, where variables are treated as coordinates in an N-dimensional space. The function's level surfaces form N-1 dimensional surfaces, and the gradient at a point defines a point in a different space. The method uses a matrix, h^μν, to represent a metric in the variable space. This matrix is updated based on the actual relationship between changes in the gradient and position. The method is divided into five parts: READY, AIM, FIRE, DRESS, and STUFF. READY establishes a search direction and evaluates the termination criterion. AIM estimates the location of the minimum within the interval. FIRE evaluates the function and gradient at the interpolated point and determines if the minimum is sufficiently located. DRESS modifies the metric matrix based on function information. STUFF tests the function's minimization and the matrix's approximation of the inverse Hessian. The method is implemented for the IBM-704 using Fortran. It has been tested with various functions and is used in least-squares calculations for experiments like π-P scattering and delayed neutron analysis. The method is efficient and can locate function minima more quickly than alternative methods. The metric matrix, h^μν, accumulates function information and compensates for ill-conditioned gradients, contributing to the method's effectiveness. The method is covariant under arbitrary linear coordinate transformations and can handle linear constraints by setting corresponding matrix elements to zero.This report describes the Variable Metric Method for minimizing differentiable functions of several variables. The method determines a matrix that characterizes the function's behavior near a minimum. For quadratic functions, no more than N iterations are needed, where N is the number of variables. The method allows for linear constraints on variables without altering the procedure. The method is based on geometric concepts, where variables are treated as coordinates in an N-dimensional space. The function's level surfaces form N-1 dimensional surfaces, and the gradient at a point defines a point in a different space. The method uses a matrix, h^μν, to represent a metric in the variable space. This matrix is updated based on the actual relationship between changes in the gradient and position. The method is divided into five parts: READY, AIM, FIRE, DRESS, and STUFF. READY establishes a search direction and evaluates the termination criterion. AIM estimates the location of the minimum within the interval. FIRE evaluates the function and gradient at the interpolated point and determines if the minimum is sufficiently located. DRESS modifies the metric matrix based on function information. STUFF tests the function's minimization and the matrix's approximation of the inverse Hessian. The method is implemented for the IBM-704 using Fortran. It has been tested with various functions and is used in least-squares calculations for experiments like π-P scattering and delayed neutron analysis. The method is efficient and can locate function minima more quickly than alternative methods. The metric matrix, h^μν, accumulates function information and compensates for ill-conditioned gradients, contributing to the method's effectiveness. The method is covariant under arbitrary linear coordinate transformations and can handle linear constraints by setting corresponding matrix elements to zero.