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Explicit function forms of hyperelliptic solutions of Korteweg-de Vries (KdV)and \break Kadomtsev-Petviashvili (KP) equations were constructed for a givencurve $y^2 = f(x)$ whose genus is three. This study was based upon the factthat about one hundred years ago (Acta Math. (1903) {\bf{27}}, 135-156), H. F.Baker essentially derived KdV hierarchy and KP equation by using bilineardifferential operator ${\bold{D}}$, identities of Pfaffians, symmetricfunctions, hyperelliptic $\sigma$-function and $\wp$-functions; $\wp_{\mu \nu}= -\partial_\mu \partial_\nu \log \sigma$ $= - ({\bold{D}}_\mu {\bold{D}}_\nu\sigma \sigma)/2\sigma^2$. The connection between his theory and the modernsoliton theory was also discussed.Comment: AMS-Tex, 12 page

Hyperelliptic solutions of KdV and KP equations: re-evaluation of Baker's study on hyperelliptic sigma functions