Book excerpt: This monograph offers a comprehensive overview of diverse quantization phenomena in layered materials, covering current mainstream experimental and theoretical research studies, and presenting essential properties of layered materials along with a wealth of figures. This book illustrates commonly used synthesis methods of these 2D materials and compares the calculated results and experimental measurements, including novel features not yet reported. The book also discusses experimental measurements of magnetic quantization, theoretical modeling for studying systems and covers diversified magneto-electronic properties, magneto-optical selection rules, unusual quantum Hall conductivities, and single- and many-particle magneto-Coulomb excitations. Rich and unique behaviors are clearly revealed in few-layer graphene systems with distinct stacking configuration, stacking-modulated structures, silicon-doped lattices, bilayer silicene/germanene systems with the bottom-top and bottom-bottom buckling structures, monolayer and bilayer phosphorene systems, and quantum topological insulators. The generalized tight-binding model, the static and dynamic Kubo formulas, and the random-phase approximation are developed/modified to thoroughly explore the fundamental properties and propose the concise physical pictures. Different high-resolution experimental measurements are discussed in detail, and they are consistent with the theoretical predictions. Aimed at readers working in materials science, physics, and engineering this book should be useful for potential applications in energy storage, electronic devices, and optoelectronic devices.