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The goal of these two lectures is to present the key ingredients of the following extension result of Y.-T.Siu [Ann.Math 102 (1975], 421-465]: let M be a compact Kähler manifold, X a complex manifold of complex dimension n, and A a closed subset of X of zero (2n-3)-Hausdorff dimension; then any meromorphic map f:X \A -->M meromorphically extends through A.