This is the first detailed account of a new approach to
microphysics based on two leading ideas: (i) the explicit
dependence of physical laws on scale encountered in quantum
physics, is the manifestation of a fundamental principle of nature,
scale relativity. This generalizes Einstein's principle of (motion)
relativity to scale transformations; (ii) the mathematical
achievement of this principle needs the introduction of a
nondifferentiable space-time varying with resolution, i.e.
characterized by its fractal properties.The author discusses in
detail reactualization of the principle of relativity and its
application to scale transformations, physical laws which are
explicitly scale dependent, and fractals as a new geometric
description of space-time.
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