The most fundamental of Hindu deities, is the Trinity of Brahma, Vishnu and Shiva - popular deities include Ganesha, Krishna, Hanuman and goddesses like Lakshmi, Durga,Saraswati.
Brahman the cosmic spirit has no linga, that is no characteristic or physical form. But it has been accepted that most worshippers need some physical form to be able to approach any god. The upright stone that is the linga is used as the symbol of the cosmic spirit.
It is said Shiva stood on one foot for several hundred thousand years transforming himself into Aja-Ekapada, the one-footed-lord, the axis of the revolving cosmos. This axis has no beginning nor an end; it is considered to be the great linga of Shiva.
According to the Mahabharata and the Matsya Purana, Shiva's linga is the divine phallus, the source of the soul-seed which contains within it the essence of the entire cosmos. From it all life is created. And when life is destroyed, it returns to the primal phallus of Shiva.
Together with the yoni-bhaga which forms its base, the linga represents the union of man and woman, Shiva and Shakti, the cosmic spirit combined with the cosmic substance that makes existence possible.