This book is devoted to the description of Bosonic and Fermionic systems: metallic clusters; quantum dots, wires, rings and molecules; trapped Fermi and Bose atoms; liquid drops of Helium; electron gas in different dimensions and geometries with and without magnetic fields.Extensively updated with 200 extra pages, the new edition of this successful book includes the field's cutting-edge areas: spin-orbit coupling in heterostructures and spintronics; the conductivity problem: conductivity of quantum wires, magnetoconductivity of nanostructures, spin-Hall conductivity; atomic Fermi gases in traps; non-collinear local spin density approximation calculations; and Brueckner-Hartree-Fock in finite size systems.