  Vandiver's conjecture states that any prime p does not divide the class
number $h(R)$ of the maximal real subfield R of the p-th cyclotomic field. The
aim of this paper is to prove Vandiver's conjecture, which has several
consequences including the first case of Fermat's Great Theorem. The main idea
lies in using relations of the algebraic K-theory and the Iwasawa theory,
discovered by M.Kervaire and M.P.Murthy in 1977.
