Algorithms for fitting free-knot splines for data with one independent variable and one dependent variable. Four free-knot spline algorithms are provided for the case where the number of knots is known in advance. A knot-search algorithm is provided for the case where the number of knots is not known in advance. In addition, methods are available to compute the fitted values, the residuals, and the coefficients of the splines, and to plot the results, along with a method to summarize the results.