Virtual synthesis of nanosystems by design : from first principles to applications Part 1. Quantum statistical mechanics fundamentals. Transport properties of spatially inhomogeneous quantum systems from the first principles Quantum properties of small systems at equilibrium : first principle calculations Part 2. Applications : electronic structure of small systems at equilibrium. Quantum dots of traditional III V semiconductor compounds Quantum dots of Gallium and Indium Arsenide Phosphides : opto electronic properties spin polarization and a composition effect of quantum confinement Quantum dots of diluted magnetic semiconductor compounds Quantum dots of Indium Nitrides Nickel oxide quantum dots and nanopolymer quantum wires Quantum dots of Indium Nitrides with special magneto optic properties Appendix. Examples of virtual templates of small quantum dots and wires of semiconductor compound elements