Mario Bonk, University of California, Los Angeles, CA.Daniel Meyer, University of Liverpool, UK.

• IntroductionThurston mapsLattes mapsQuasiconformal and rough geometryCell decompositionsExpansionThurston maps with two or three postcritical pointsVisual metricsSymbolic dynamicsTile graphsIsotopiesSubdivisionsQuotients of Thurston mapsCombinatorially expanding Thurston mapsInvariant curvesThe combinatorial expansion factorThe measure of maximal entropyThe geometry of the visual sphereRational Thurston maps and Lebesgue measureA combinatorial characterization of Lattes mapsOutlook and open problemsAppendix ABibliographyIndex.

Mario Bonk, University of California, Los Angeles, CA.Daniel Meyer, University of Liverpool, UK.

• IntroductionThurston mapsLattes mapsQuasiconformal and rough geometryCell decompositionsExpansionThurston maps with two or three postcritical pointsVisual metricsSymbolic dynamicsTile graphsIsotopiesSubdivisionsQuotients of Thurston mapsCombinatorially expanding Thurston mapsInvariant curvesThe combinatorial expansion factorThe measure of maximal entropyThe geometry of the visual sphereRational Thurston maps and Lebesgue measureA combinatorial characterization of Lattes mapsOutlook and open problemsAppendix ABibliographyIndex.

Mario Bonk, University of California, Los Angeles, CA.Daniel Meyer, University of Liverpool, UK.

• IntroductionThurston mapsLattes mapsQuasiconformal and rough geometryCell decompositionsExpansionThurston maps with two or three postcritical pointsVisual metricsSymbolic dynamicsTile graphsIsotopiesSubdivisionsQuotients of Thurston mapsCombinatorially expanding Thurston mapsInvariant curvesThe combinatorial expansion factorThe measure of maximal entropyThe geometry of the visual sphereRational Thurston maps and Lebesgue measureA combinatorial characterization of Lattes mapsOutlook and open problemsAppendix ABibliographyIndex.