The book presents a mathematical formulation of sedimentation processes and shows how this theory can be applied to design and control of continuous thickeners. A distinctive feature of the book is a combination of rigorous axiomatic phenomenological approach with applications to important practical problems. The mathematical model of sedimentation and exact and approximate solutions for problems encountered in laboratory and in industry can be found in chapters 1-3, 7, 8 and 10-12, whereas chapters 4-6 and 9 show recent results on the conservation laws for quasilinear hyperbolic and degenerate parabolic equations of interest.