Textbook in PDF format In recent years there has been considerable interest in studying the DENSITY-OF-STATES (DOS) functions and Related Applications in Quantized Structures of different technologically important materials in low dimensional electronics. The concept of DOS function is of fundamental importance for not only the characterization of semiconductor nanostructures but also in the study of the carrier transport in quantum effect devices. The acoustic mobility limited momentum relaxation time is inversely proportional to the respective DOS function of a particular semiconductor and the DOS function, in turn, is connected to the twenty five important transport topics of quantum effect devices namely the Landau Dia and Pauli's Para Magnetic Susceptibilities, the Einstein's Photoemission, the Einstein Relation, the Debye Screening Length, the Generalized Raman gain, the Normalized Hall coefficient, the Fowler-Nordheim Field Emission, the Gate Capacitance, the Thermoelectric Power, the Plasma Frequency, the Magneto-Thermal effect in Quantized Structures, the Activity coefficient, the Reflection coefficient, the Heat Capacity, the Faraday rotation, the Optical Effective Mass, the Carrier contribution to the elastic constants, the Diffusion coefficient of the minority carriers, the Nonlinear optical response, the Third order nonlinear optical susceptibility, the Righi-Leduc coefficient, the Electric Susceptibility, the Electric Susceptibility Mass, the Electron Diffusion Thermo-power and the Hydrostatic Piezo-resistance Coefficient respectively