"Focus is on the topics suggested by the title: Quantization in its various aspects, Poisson brackets and generalizations, and structures "beyond", including symplectic supermanifolds, operads, Lie groupoids and Lie (bi)algebroids and algebras with n-ary operations. This book offers accounts of new results as well as accessible expositions useful to a broad reading audience of researchers in differential geometry, algebraic topology and mathematical physics."--BOOK JACKET.