This is the first detailed account of a new approach to microphysics based on two leading ideas: that the explicit dependence of physical laws on scale encountered in quantum physics, is the manifestation of a fundamental principle of nature, namely, scale relativity (this generalizes Einstein's principle of (motion) relativity to scale transformations); and that 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...