Learning and decisions are precise functional states of brain cortical circuits that can only be approached by the use of multidisciplinary and complementary tools. The availability of genetically manipulated mice and rats, of mathematical and computational neuroscience methods, and of advanced electrophysiological techniques  susceptible of being applied in behaving animals during the acquisition of different learning paradigms  has largely facilitated this approach. Here, we have recorded activity-dependent changes in synaptic strength in different synapses of hippocampal and prefrontal circuits during the acquisition and storage of classical and instrumental conditioning paradigms. Furthermore, we have developed a dynamic approach of multisynaptic state functions to characterize the acquisition of new motor and/or cognitive skills. In our opinion, a synaptic state function is analogous to a precise picture of a synaptic contact while the behaving animal learns the selected task. Therefore, the different state functions of large cortical synaptic circuits during the very moment at which learning is taking place could be specifically defined by 3D-arrays of synaptic sites, learning stages, and behaviors. The couplings among the different synaptic state functions were determined by means of weight functions that characterized the changes in synaptic strengths, the type (linear or nonlinear) of interdependences among state functions, as well as the timing and correlation relationships among them. The detailed analysis of the collected data indicates that many synaptic sites within cortical circuits modulate their synaptic strength across the successive stages of acquisition of associative learning tasks. The main output of this study is that learning is the result of the activity of wide cortical and subcortical circuits activating particular functional properties of involved synaptic nodes, and that we can quantify that activation pattern by means of state and weight functions. In this regard, we expect that a map of state functions relating the acquisition of new motor and cognitive abilities and the underlying synaptic plastic changes will be offered in the near future for different types of learning tasks and situations. This same optimized approach could be applied to the selective stimulation of synaptic nodes across the involved circuits, in genetically modified animals or in animals receiving selective injections of si-RNA, and other molecular-disturbing procedures.