The present work is a theoretical ab initio study of silicon (mainly) and silicon-based or “silicon-like” Nanocrystals and nanostructures, such as core/shell quantum dots and ultra-thin nanowires of Si, Ge, and Sn. The main focus is on the quantum confinement of Si quantum dots and the description of their structural, cohesive, electronic, and optical properties in terms of size, growth pattern and surface conditions. An important outcome of such study, besides the very satisfactory agreement with experimental measurements for nanocrystals (up to 32 Å in diameter), is the judicious extrapolation of the nanoscale results all the way to infinite silicon crystal, and the successful comparison with experiment (for both the energy gap and the cohesive energy of crystalline silicon). This is an additional verification for the essential correctness of our approach. Our present results, which are based on earlier findings of prof. Zdetsis’ group for spherical Si quantum dots, are in full agreement with those results and predictions. We have expanded our study to selective cases of pure C, Ge, Sn and their mixed nanocrystals and nanowires. Thus, the classes of systems studied here include: a) Silicon quantum dots terminated by hydrogen of three different growth models (spherical, elongated, and reconstructed) without and with oxygen “contamination” of four different modes (double bonds, bridging single bonds, hydroxyl formation and mixed modes). b) Analogous quantum dots, pure and mixed (core/shell) of C, Si, Ge, and Sn. c) Ultrafine silicon and germanium nanowires of various growth patterns. The majority of this work is based in density functional theory (DFT), both ground state and time-depended, using in most cases the hybrid functional of Becke, Lee, Parr and Yang (B3LYP), and in several places the PBE and PBE0 functionals. A limited number of calculations was performed with post SCF methods, such as many-body perturbation theory (MP2) or Coupled cluster CCSD(T), for comparison. For the study of Si and Ge nanowires we have also used properly selected (and tested) semiempirical methods and calculations. These theoretical methods and techniques are reviewed in considerable detail in the first three chapters (Part I) of the present thesis. The results of the calculations are discussed in Part II, divided in three Chapters (4-6). Chapter 4 is devoted to the structural, electronic, cohesive and elastic properties of ultrafine hydrogenated silicon and germanium nanowires. Chapter 5 describes the influence of the growth patterns and surface conditions on structural, cohesive, and electronic properties of silicon nanocrystals, as well as their size dependence all the way to infinity. This (very successful) size dependence, in full accord with quantum confinement, is also compared with the (poor) predictions of the BOLS correlation scheme. Finally, Chapter 6 deals with carbon, silicon, germanium, tin and their mixed core/shell quantum dots. / --