  Charge conjugation C is one of the fundamental symmetries in nature which
transforms particles into antiparticles. This symmetry was studied in weak
interaction where it is fully violated, but it is poorly known in the strong
and electromagnetic interactions.
  To this end, in this thesis we investigated eta->pi+pi-pi0 and eta->pi0 e+e-
decays, which might violate charge conjugation symmetry. The violation of C
symmetry in eta->pi+pi-pi0 process could manifest itself as an asymmetry
between energy spectra of charged pions. The eta->pi0 e+e- decay is forbidden
by C symmetry in the first order of electromagnetic interaction, with the
branching ratio on a level of 10^-8. Therefore, observation of a larger
branching ratio could indicate a mechanism involving first order
electromagnetic interaction violating charge conjugation.
  Both decays were investigated by means of the WASA-at-COSY detector operating
at the COSY synchrotron at the Forchungszentrum Julich in Germany. The eta
meson was produced via pp->pp eta reaction at the proton beam momentum of
2.14GeV/c. In total around 5x10^7 eta mesons were collected.
  As a result of the analysis conducted in the framework of this thesis a
Dalitz Plot distribution for the eta->pi+pi-pi0 decay was obtained. From this
distribution we extracted asymmetry parameters sensitive to C symmetry
violation for different isospin values of the final state and we have
established that all are consistent with zero within the obtained accuracy.
  For the eta->pi0 e+e- decay we have not observe signal and thus we estimated
an upper limit for the branching ratio. The established upper limit amounts to
$BR(eta->pi0 e+e-)<3.7x10^-5 at the 90% confidence level. This result is more
precise than previously obtained in other experiments.
