  We report results of a multi-frequency (0.8-60 GHz) electron spin resonance
study of the spin dynamics in the quasi-2D square lattice antiferromagnet
Ba$_2$MnGe$_2$O$_7$ both in antiferromagnetically ordered and paramagnetic
phases. We directly observe two zero-field gaps in the excitation spectrum of
the ordered phase, the larger one being due to easy-plane anisotropy, and the
smaller one indicates the presence of fourth-order in-plane anisotropy probably
related to the multiferroic properties of this compound. We observe effects of
hyperfine interaction on the electron spin resonance spectra in the
antiferromagnetically ordered state, which turns out to be comparable with
in-plane anisotropy. The hyperfine field strength is found from the observed
low-temperature electron spin resonance data. The spin dynamics of the
paramagnetic phase is characterized by strong broadening of the ESR absorption
line, which can be ascribed to the vortex dynamics of a 2D magnet.
