  This paper represents the main portion of the Ph.D. Thesis of the author, and
is the first of the series of four papers, which is a joint work with K.
Matsuki as a whole. We present a program toward constructing an algorithm for
resolution of singularities in positive characteristic. We would like to
emphasize, however, that the program is actually valid in all characteristics.
As such, it leads in characteristic zero to a complete algorithm, which is
slightly different from the existing ones. In positive characteristic, almost
all the ingredients work nicely forming a perfect parallel to the case in
characteristic zero, except for the problem of termination, which remains as
the only missing piece toward the completion of our algorithm.
