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Curve fitting is the process of constructing a curve that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data. Fitted curves can be used as an aid for data visualization, to infer values of a function where no data are available, and to summarize the relationships among two or more variables. Extrapolation refers to the use of a fitted curve beyond the range of the observed data, and is subject to a degree of uncertainty since it may reflect the method used to construct the curve as much as it reflects the observed data.This book is devoted on the qualitative theory of quantum curve fittings. The book is intended for senior undergraduate students and beginning graduate students of engineering and science courses. There are four chapters in this book. The chapters in the bookare pedagogically organized. Each chapter concludes with a section with practical problems.