Redman is distinguished for original and highly skilful advances in the quantitative analysis of transmission mechanisms between nerve fibres and their target cells. Applying his background in mathematics and electrical engineering, he solved the equations describing spread of excitatory current in complex nerve and muscle cells, and developed new procedures for analysing their passive electrical properties, including those of the geometrically highly complex spinal motoneurone. By recording responses of one motoneurone to impulses in a single presynaptic nerve fibre, both subsequently labelled and visualized histochemically, he has succeeded in relating the precise location and number of the endings of a single presynaptic fibre to the quantitatively analysed excitatory action of single impulses therein. This unique achievement, together with his earlier mathematical modelling, is recognized internationally and qualifies Redman as a leading authority on excitatory synaptic transmission.