The axon of inferior olive neuron that projects to the cerebellar cortex, largely via the inferior cerebellar peduncle. They range in diameter from 1-3 um and are myelinated until they enter the granule cell layer. They give off collaterals to the deep cerebellar nuclei. They synapse extensively with the dendrites of Purkinje cells in the molecular layer, where each fiber branches repeatedly to "climb" along the Purkinje cell dendritic tree. Each Purkinje cell is innervated by only a single climbing fiber.