  In May-June 2014, the experiment devoted to the search for the bound state of
the $\eta$ meson and $^3$$He$ nucleus has been performed at COSY accelerator in
Research Center J\"ulich in Germany with WASA-at-COSY facility.
  The excitation functions for $pd\rightarrow^3$$He2\gamma$,
$pd\rightarrow^3$$He6\gamma$, $pd\rightarrow ppp\pi^{-}$, $pd\rightarrow
ppn\pi^{0}$, $pd\rightarrow dn\pi^{-}$, $pd\rightarrow dp\pi^{0}$,
$pd\rightarrow pd$, and $pd\rightarrow ppn$ reactions have been measured in the
vicinity of the $\eta$ meson production threshold. The experiment was carried
out using COSY ramped proton beam and deuterium pellet target. The beam
momentum varied continuously in the range of $1.426-1.635~GeV/c$ corresponding
to $^3$$He-\eta$ excess energy range from $-70$ to $+30~MeV$.
  The analysis of the obtained excitation functions for the
$pd\rightarrow^3$$He\eta$ indicate slightly the signal from the bound state for
$\Gamma>20~MeV$ and $B\in[0;15]~MeV$. However, the observed indication is in
the range of the systematic error. Therefore the final conclusion of this
thesis is that no narrow structure that could be interpreted as $\eta$-mesic
nucleus was observed in both excitation curves. Thus, the upper limit for the
total cross section of the bound state formation was estimated assuming that
the $\eta$ decay branching ratios in the bound state is the same as in free
space. The upper limit at the $90\%$ confidence level varies from $2$ to
$15~nb$ within the binding energy range from $0$ to $60~MeV$ and the width from
$2.5$ to $40~MeV$.
