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Abstract：Let $G$ and $H$ be two simple graphs. A  bijection $\phi:V(G)\rightarrow V(H)$ is called an {\it isomorphism} between $G$  and $H$ if $(\phi\hspace{0.5mm} v_i)(\phi\hspace{0.5mm} v_j)\in E(H)$  $\Leftrightarrow$ $v_i v_j\in E(G)$ for any two vertices $v_i$ and $v_j$ of $G$.  As well-known, the problem of determining whether or not two given graphs are  isomorphic is called {\it Graph Isomorphism Problem}. In this talk we shall  present some new approaches developed for GI and a deterministic algorithm  solving Graph Isomorphism Problem in time $n^{ O( \log n ) }$.