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We investigate the decay property of the eigenvalues of theNeumann-Poincar\'{e} operator in two dimensions. As is well-known, thisoperator admits only a sequence of eigenvalues that accumulates to zero as itsspectrum for a bounded domain having $C^{1,\alpha}$ boundary with $\alpha\in(0,1)$. In this paper, we show that the eigenvalue $\lambda_k$'s of theNeumann-Poincar\'{e} operator ordered by size satisfy that $|\lambda_k| =O(k^{-p-\alpha+1/2})$ for an arbitrary simply connected domain having$C^{1+p,\alpha}$ boundary with $p\geq 0,~ \alpha\in(0,1)$ and$p+\alpha>\frac{1}{2}$.

A decay estimate for the eigenvalues of the Neumann-Poincar\'{e} operator in two dimensions using the Grunsky coefficients