The human genotype represents at most ten billion pieces of binary information, whereas the humain brain contains more than a million times a billion synapses. So a differentiated brain structure is due to synaptic self-organization and adaptation. The goal is to model the formation of observed global brain structures and cognitive properties from local synaptic dynamics sometimes supervised by the limbic system. A general-neurosynaptic dynamics is solved with a novel field theory in a comprehensible manner and in quantitative agreement with many observations. Novel results concern for instance thermal membrane fluctuations, fluctuation dissipation theorems, cortical maps, topological charges, operant conditioning, transitive inference, learning hidden structures, behaviourism, attention focus, Wittgenstein paradox, infinite generalization, schizophrenia dynamics, perception dynamics, non- equilibrium phase transitions, emergent valuation. Also the formation of advanced cognitive properties is modeled.