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Explicit hyperelliptic solutions of the modified Korteweg-de Vries equationswithout any ambiguous parameters were constructed in terms only of thehyperelliptic $\al$-functions over non-degenerated hyperelliptic curve $y^2 =f(x)$ of arbitrary genus $g$. In the derivation, any $\theta$-functions orBaker-Akhiezer functions were not essentially used. Then the Miuratransformation naturally appears as the connections between the hyperelliptic$\wp$-functions and hyperelliptic $\al$-functions.Comment: AMS-Tex, 13 page

Hyperelliptic solutions of modified Korteweg-de Vries equation of genus g: essentials of the Miura transformation