  Bose-Einstein condensation (BEC) is a quantum phenomenon of formation of the
collective quantum state, in which the macroscopic number of particles occupies
the lowest energy state and thus is governed by a single wave function. Here we
highlight the BEC in a magnetic subsystem -- the BEC of magnons, elementary
magnetic excitations. Magnon BEC is manifested as the spontaneously emerging
state of the precessing spins, in which all spins precess with the same
frequency and phase even in the inhomogeneous magnetic field. We consider this
phenomenon on example of spin precession in superfluid phases of $^3$He. The
magnon BEC in these phases has all the properties of spin superfluidity. The
states of the phase-coherent precession belong to the class of the coherent
quantum states, which manifest themselves by superfluidity, superconductivity,
quantum Hall effect, Josephson effect and many other macroscopic quantum
phenomena.
