Noncommutative geometry is a novel approach which is opening up new possibilities for geometry from a mathematical viewpoint. It is also providing new tools for the investigation of quantum space-time in physics. Recent developments in string theory have supported the idea of quantum spaces, and have strongly stimulated the research in this field. This self-contained volume contains survey lectures and research articles which address these issues and related topics. The book is accessible to both researchers and graduate students beginning to study this subject.Contents:Deformations and Noncommutativity:Expressions of Algebra Elements and Transcendental Noncommutative Calculus (H Omori et al.)Representations of Gauge Transformation Groups of Higher Abelian Gerbes (K Gomi)Examples of Groupoid (N Miyazaki)Differential Equations and Schwarzian Derivatives (H Sato et al.)Deformed Field Theory and Solutions:Noncommutative Solitons (O Lechtenfeld)Seiberg–Witten Monopole and Young Diagrams (A Sako)Instantons in Non(anti)commutative Gauge Theory via Deformed ADHM Construction (T Araki et al.)A Solution of Yang–Mills Equation on BdS Spacetime (X Ren & S Wang)Difference Discrete Geometry on Lattice (K Wu et al.)and other papersReadership: Graduate students and researchers in mathematics and theoretical physics.