The projective unitary representations of the symplectic group \(\mathrm{Sp}(n,\mathbb{R})\), called metaplectic representations or Weyl representations, play an important role in mathematics and quantum mechanics. The group \(\mathrm{Sp}(n,\mathbb{R})\) identified to a subgroup \(S\) of \(\mathrm{SU}(n,n)\) acts on the \((2n+1)\)-dimensional Heisenberg group \(H_n\) and on the non-degenerated unitary irreducible representations \(\varrho\) of \(H_n\) on the Fock space \(\mathcal{F}\). For any \(k\in S\) and \(\varrho\), the representations \(k \cdot \varrho\) and \(\varrho\) are unitarily equivalent, that is, there exists a unitary operator \(\sigma(k):\mathcal{F} \rightarrow \mathcal{F}\) such that \((k\cdot \varrho)(h) \sigma(k)=\sigma(k)\, \varrho(h)\), for any \(h\in H_n\). The map \(k\mapsto k\cdot \varrho\) is the metaplectic representation of \(\mathrm{Sp}(n,\mathbb{R})\). The author describes in full details the kernels of the operators \(\sigma(k)\) and their Berezin symbols. Explicit formulas are also given for the complex Weyl symbols \(W_0(\sigma(k))\) of the metaplectic operators \(\sigma(k)\) obtained using the correspondence \(W_0\) between the operators \(A:\mathcal{F}\rightarrow \mathcal{F}\) and functions on \(\mathbb{C}^n\), called complex Weyl calculus. Several applications of the obtained formulas are presented in the second part of the paper.