An accessible text for the study of numerical methods for solving least squares problems remains an essential part of a scientific software foundation. Numerical analysts, statisticians, and engineers have developed techniques and nomenclature for the least squares problems of their own discipline. This well-organized presentation of the basic material needed for the solution of least squares problems helps to unify this divergence of methods. Mathematicians, practicing engineers, and scientists will welcome its return to print. The material covered includes Householder and Givens orthogonal transformations, the QR and SVD decompositions, equality constraints, solutions in nonnegative variables, banded problems, and updating methods for sequential estimation. Both the theory and practical algorithms are included. The easily understood explanations and the appendix providing a review of basic linear algebra make the book accessible for the nonspecialist. This Classic edition includes a new appendix that summarizes the major developments since the book was originally published in 1974. The additions are organized in short sections associated with each chapter. An additional 230 references have been added, bringing the bibliography to over 400 entries. Appendix C has been edited to reflect changes in the associated software package and software distribution method. The software has been upgraded to conform to the FORTRAN 77 standard and a new subroutine has been added in FORTRAN 90 for the solution of the bounded variables least squares problem (BVLS). The codes are available from netlib via the Internet.