  The modern theories of Grand Unification (GUT) and supersymmetric (SUSY)
extensions of standard model (SM) suppose that the conservation laws of the SM
may be violated to some small degree. The nuclei are well-suited as a
laboratory to test fundamental symmetries and fundamental interactions like
lepton flavor (LF) and lepton number (LN) conservation. A prominent role
between experiments looking for LF and total LN violation play yet not observed
processes of neutrinoless double beta decay. The GUT's and SUSY models offer a
variety of mechanisms which allow this process to occur. They are based on
mixing of Majorana neutrinos and/or R-parity violation hypothesis. Although the
neutrinoless double beta decay has not been seen it is possible to extract from
the lower limits of the lifetime upper limits for the effective electron
Majorana neutrino mass, effective right handed weak interaction parameters, the
effective Majoron coupling constant, R-parity violating SUSY parameters etc.
  In this work the limits on the LN violating parameters extracted from current
neutrinoless double beta decay experiments are listed. Studies in respect to
future neutrinoless double beta decay experimental projects are also presented.
