The fitting of a curve or surface through a set of observational data is a very frequent problem in different disciplines (mathematics, engineering, medicine, ...) with many interesting applications. This book describes the algorithms and mathematical fundamentals of a widely used softwarepackage for data fitting with (tensor product) splines. As such it gives a survey of possibilities and benefits but also of the problems to cope with when approximating with this popular type of function. In particular it is demonstrated in detail how the properties of B-splines can be fullyexploited for improving the computational efficiency and for incorporating different boundary or shape preserving constraints. Special attention is also paid to strategies for an automatic and adaptive knot selection with intent to obtain serious data reductions. The practical use of the smoothingsoftware is illustrated with many examples, academic as well as taken from real life.