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This unique reference, aimed at research topologists, gives an exposition of the 'pseudoAnosov' theory of foliations of 3manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in 1dimensional and codimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as traintracks, branched surfaces and hierarchies to carry more complicated continuous objects.
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