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Let the sample correlation matrix be $W=YY^T$, where $Y=(y_{ij})_{p,n}$ with$y_{ij}=x_{ij}/\sqrt{\sum_{j=1}^nx_{ij}^2}$. We assume $\{x_{ij}: 1\leq i\leqp, 1\leq j\leq n\}$ to be a collection of independent symmetric distributedrandom variables with sub-exponential tails. Moreover, for any $i$, we assume$x_{ij}, 1\leq j\leq n$ to be identically distributed. We assume $0<p<n$ and$p/n\rightarrow y$ with some $y\in(0,1)$ as $p,n\rightarrow\infty$. In thispaper, we provide the Tracy-Widom law ($TW_1$) for both the largest andsmallest eigenvalues of $W$. If $x_{ij}$ are i.i.d. standard normal, we canderive the $TW_1$ for both the largest and smallest eigenvalues of the matrix$\mathcal{R}=RR^T$, where $R=(r_{ij})_{p,n}$ with $r_{ij}=(x_{ij}-\barx_i)/\sqrt{\sum_{j=1}^n(x_{ij}-\bar x_i)^2}$, $\barx_i=n^{-1}\sum_{j=1}^nx_{ij}$.

Tracy-Widom law for the extreme eigenvalues of sample correlation matrices