The basic properties of the neutron are discussed in the context of the applications of neutron scattering in studies of the magnetic properties of condensed matter. A general cross section for magnetic neutron scattering from unpaired electrons is given. The characteristic features of the cross section are discussed in terms of its sensitivity to the spin correlations, both in space and time. The elastic neutron scattering provides information about the arrangement of the magnetic moments in an atomic scale. These orderings may be paramagnetic, short-range order spin-glass type, or long range order like: ferromagnetic, ferrimagnetic, antiferromagnetic or modulated. Elastic scattering provides also important information about the coherence length of the magnetic ordering and it may be also used to study magnetic ordering in 2 dimensional planes as well as orderings along 1 dimensional chains. The kinetic energy of thermal and cold neutrons is comparable to the energy of elementary excitations in condensed matter between about few to hundreds of meV. Inelastic neutron scattering, associated with changes of both, momentum and kinetic energy of the neutron, can be used in studies of elementary excitations in solids (e.g. magnons). Inelastic neutron scattering studies of magnetic excitations of the electronic and nuclear spin systems are discussed.