The goal of this new edition is to fix typographical errors found in the second edition, update coverage of material to eliminate out-of-date material and add new material of interest, and revise exposition of certain material. The author updated the primer on computer arithmetic in Chapter 1 to better reflect reality, updated the brief history of computing, and revised the section on roots of polynomials to reflect things the author has learned since 2013. The author added a new subsection on Higher-Order Difference Methods and added new material to the section on Broyden's Method.  There is new material on Jacobi-based methods, bisection and inertia, higher order difference methods, and multigrid ideas. Finally, the author also added new material to the section on radial basis function interpolation and spectral methods for higher-dimensional problems. Fundamental numerical analysis tools are introduced in Chapter 2 and then used throughout the remainder of the text.