Introduction. The Advent of Ultrathin, Well-Contained Semiconductor Heterostructures. A Prerequisite. The Mastering of Semiconductor Purity and Interfaces. The Electronic Properties of Thin Semiconductor Heterostructures. Quantum Well Energy Levels. Triangular Quantum Well Energy Levels. Two-Dimensional Density of States. Excitons and Shallow Impurities in Quantum Wells. Tunneling Structures, Coupled Quantum Wells, and Superlattices. Modulation Doping of Heterostructures. n-i-p-i Structures. Optical Properties of Thin Heterostructures. Optical Matrix Element. Selection Rules. Energy Levels, Band Discontinuities, and Layer Fluctuations. Low Temperature Luminescence. Carrier and Exciton Dynamics. Inelastic Light Scattering. Non-Linear and Electro-Optic Effects. Electrical Properties of Thin Heterostructures. Mobility in Parallel Transport. Hot Electron Effects in Parallel Transport. Perpendicular Transport. Quantum Transport. Applications of Quantized Semiconductor Heterostructures. Electronic Devices Based on Parallel Transport. Electronic Devices Based on Perpendicular Transport. Quantum Well Lasers. Towards 1D and 0D Physics and Devices. One- and Zero-Dimensional Systems. 1D and 0D Semiconductor Fabrication Techniques. Electrical Applications of 1D and 0D Structures. 1D and 0D Optical Devices. Selected Bibliography. References. Index.