  We devise a new geometric approach to study the propagation of disturbance -
compactly supported data - in reaction diffusion equations. The method builds a
bridge between the propagation of disturbance and of almost planar solutions.
It applies to very general reaction-diffusion equations. The main consequences
we derive in this paper are: a new proof of the classical Freidlin-Gartner
formula for the asymptotic speed of spreading for periodic Fisher-KPP
equations, extension of the formula to the monostable, combustion and bistable
cases, existence of the asymptotic speed of spreading for equations with almost
periodic temporal dependence, multilevel propagation for multistable equations.
