The study of mapping class groups, the moduli space of Riemann surfaces, Teuchmuller geometry and related areas has an advantage in its number of experienced scholars and at the same time the increasing number of those new to the field. To get them closer together, this collection of papers focuses on open problems and directions. Topics include cohomological combinatorial and algebraic structure, including finiteness and Torelli spaceshomomorphisms, and probing with arcs, connections with 3-manifolds, symplectic geometry and algebraic geometry, including problems in Heegaard distance and Lefschetz pencils, geometric and dynamical aspects, including problems on billiards and Weil-Petersson perspectives, and braid groups and other related groups, including Iwahori-Heck algebras and free Abelian groups. Papers include exercises and references. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)