Magnetic properties of individual nanoparticles, their ensembles, nano
composites and nanocrystalline homogeneous ferromagnets are reviewed.
Size effects in the intrinsic magnetic properties (Curie-temperature,
saturation magnetization) and in the domain magnetism (coercitivity, h
ysteresis, remanence) are treated from elementary basic principles to
the description of complex systems such as interacting magnetic cluste
rs. By examples taken form the recent literature the most hot topics o
f the field are illustrated, and more recent or expected applications
are also mentioned.