This novel book on scientific and engineerng numerical computation is intended to be used by the non-expert student or researcher. The presentation is rigorous enough so that the reader will not be frustrated or misled, but practical enough, so that the gap between theory and practice is not wide. The book discusses the fundamental and practical issues involved in a numerical computation in a unified manner with a generous, but not excessive, dose of thetheory. It concisely illustrates the practical implementation of the numerical algorithms and demysifies many seemingly esoteric numerical methods. Numerical methods that can be explained without too much elaboration and implemented within a few dozen lines of computer code are discussed in detail. Numericalmethods whose underlying theory requires long, elaborate explanations and algorithms not likely to be used without resorting to numerical packages are discussed at the level of first principles, but arenot explained in detail; however, references for further information are given. The numerical methods discussed are actually used in practice. Long equations and specialized notation are avoided as much as possible; instead, the presentation relies on schematic illustrations,not formally designated as figures, accompanying the text. The interplay between ideas and visual images is an important aspect of the discourse. Numerical examples are presented when it was judged that it would be difficult for the readers to produce their own. A bonus is an accompanying library of FORTRAN programs,freely accessible through the internet.