Noncommutative Polynomial Algebras of Solvable Type and Their Modules is the first book to systematically introduce the basic constructive-computational theory and methods developed for investigating solvable polynomial algebras and their modules. In doing so, this book covers: A constructive introduction to solvable polynomial algebras and Grbner basis theory for left ideals of solvable polynomial algebras and submodules of free modulesThe new i ltered-graded techniques combined with the determination of the existence of graded monomial orderingsThe elimination theory and methods (for left ideals and submodules of free modules) combining the Grbner basis techniques with the use of Gelfand-Kirillov dimension, and the construction of dii erent kinds of elimination orderingsThe computational construction of i nite free resolutions (including computation of syzygies, construction of dii erent kinds of i nite minimal free resolutions based on computation of dii erent kinds of minimal generating sets), etc.This book is perfectly suited to researchers and postgraduates researching noncommutative computational algebra and would also be an ideal resource for teaching an advanced lecture course.