  Some magnets due to particular geometry of the exchange bonds do not undergo
transition to the conventional magnetically ordered state despite of the
presence of significant exchange couplings. Instead, a collective paramagnetic
state is formed. The later state can remain stable down to $T=0$ if the ground
state of this magnet turns out to be nonmagnetic singlet separated from the
excited triplet states by an energy gap. Low-temperature spin dynamics of the
collective paramagnets with gapped excitations spectrum (or spin-gap magnets)
can be described in terms of a dilute gas of the triplet excitations. Applied
magnetic field can suppress the energy gap, resulting in the formation of the
gapless spin-liquid state or even leading to the unusual phenomenon of
field-induced antiferromagnetic order. Introduction of defects in the
crystallographic structure of the spin-gap magnet can result either in the
formation of multi-spin paramagnetic center or in the formation of randomly
distributed modified exchange bonds in the crystal. This review includes
results of electron spin resonance (ESR) spectroscopy study of several
representative quantum paramagnets with gapped excitations spectrum:
quasy-two-dimensional magnet \phcc{}, quasy-one-dimensional magnets of
"spin-tube" type \sul{} and "spin-ladder" type \dimpy{}. We will demonstrate
that ESR absorption spectra reveal common features of these systems: ESR
spectroscopy allows to observe and characterize fine structure if the triplet
energy levels, to identify many-particles relaxation processes in the gas of
triplet excitations and to observe collective spin-wave oscillations in the
field induced antiferromagnetically ordered state, as well as to observe some
individual features of the studied systems.
