A conceptual framework is developed for the quantitative analysis of signal transfer through cellular signal transduction pathways and networks. This approach is referred to as signal transfer analysis and is based on formalisms that were first developed for the analysis of metabolic networks. Signal transduction is quantified as the sensitivity, known as the response coefficient of a target (e.g. an ion channel or transcription factor) to a signal (e.g. a hormone, growth factor or neurotransmitter). This response coefficient is defined in terms of the fractional change in the activated target brought about by a small fractional change in the signal. Quantifying the signal transduction in this way makes it possible to prove that for an idealized signaling cascade without feedback loops, the total response equals the product of all the local response coefficients, one for each level of the cascade. We show under which conditions merely having more levels in a cascade can boost the sensitivity of a target to a signal. If a signal propagates to a target through two different routes, these routes contribute independently to the total response, provided there is no feedback from the target. This independence makes the behavior of signaling cascades different from that of metabolic pathways, where different branches are connected through Kirchhoffs law. The relations between the total response and the local kinetics at each level are given for a number of network structures, such as branched signaling pathways and pathways with feedback. The formalism introduced here may provide a general approach to quantify cellular information transfer.