This book deals with the application of fractal and nonlinear time-series analysis to seismicity and earthquakes within the framework of earthquake prediction research. Emphasis is on theoretical foundations as well as practical implementation and pitfalls to enable readers to conduct their own analyses. The theoretical parts include introductions to fractals and multifractals, the relation between fractal dimension and entropy, the Hurst phenomenon, basic ideas of low-dimensional chaotic dynamics and a roadmap of nonlinear time-series analysis. Practical implementation is discussed in each case and synthetic data sets are analyzed. Fractal methods are applied to landslide and seismicity patterns in space and time, nonlinear analysis is carried out for radon and strain data as well as earthquake intervals. Due to the comprehensive coverage of theoretical background and step-by-step applications, readers of all levels will benefit from this book.