  The mathematical basis of p-adic Higgs mechanism discussed in papers
<EMAIL_ADDRESS>9410058-62 is considered in this paper. The basic
properties of p-adic numbers, of their algebraic extensions and the so called
canonical identification between positive real numbers and p-adic numbers are
described. Canonical identification induces p-adic topology and differentiable
structure on real axis and allows definition of definite integral with
physically desired properties. p-Adic numbers together with canonical
identification provide analytic tool to produce fractals. Canonical
identification makes it possible to generalize probability concept, Hilbert
space concept, Riemannian metric and Lie groups to p-adic context. Conformal
invariance generalizes to arbitrary dimensions since p-adic numbers allow
algebraic extensions of arbitrary dimension. The central theme of all
developments is the existence of square root, which forces unique algebraic
extension with dimension $D=4$ and $D=8$ for $p>2$ and $p=2$ respectively. This
in turn implies that the dimensions of p-adic Riemann spaces are multiples of
$4$ in $p>2$ case and of $8$ in $p=2$ case.
