This book will aid readers in developing problem-solving skills for making judicious method selections. The chapters may be read independently. Appendices A and B include basic methods of convergence acceleration and details of computing the solutions to very high accuracy. Full code for all the methods, examples, tables, and figures is given (partly in Appendix C, completely on the accompanying web page). The code is written in a variety of languages, including Mathematica, Matlab, Maple, C, Octave, and PARI/GP. Appendix D offers a sample of additional challenging problems for those who master some of the techniques discussed here.