Fractals: A User's Guide for the Natural Sciences explains Mandelbrot's fractal geometry and describes some of its applications in the natural world. Written to enable students and researchers to master the methods of this timely subject, the book steers a middle course between the formality of many papers in mathematics and the informality of picture-oriented books on fractals. It is both a logically developed text and a `fractals for users' handbook. Fractal geometry exploits a characteristic property of the real world self-similarity - to find simple rules for the assembly of complex natural objects. Beginning with the foundations of measurement in Euclidean geometry, the authors progress from analogues in the geometry of random fractals to illustrative applications spanning the natural sciences: the developmental biology of neurons and pancreatic islets; fluctuations of bird populations; patterns in vegetative ecosystems; and even earthquake models. The final section provides a toolbox of user-ready programs. This volume is an essential resource for all natural scientists interested in working with fractals.