Nataraja is the form of Shiva as the cosmic dancer, who performs the tandava, the dance of creation and destruction. He is depicted with four arms, holding a drum, a fire, a trident and a gesture of fearlessness, surrounded by a ring of flames.
Lingam is the aniconic representation of Shiva as the supreme reality, the essence of all things. It is usually a cylindrical pillar with a rounded top, often placed on a yoni, a base symbolizing the feminine counterpart of Shiva. Lingam is the object of worship in many temples and shrines dedicated to Shiva.
Ardhanarishvara is the form of Shiva as the composite of both male and female, representing the synthesis of the dual aspects of reality. He is depicted as half-Shiva and half-Parvati, the goddess consort of Shiva, sharing one body and one head, but with distinct attributes and attire.
Rudra is the form of Shiva as the fierce and destructive aspect of the Supreme, the lord of storms, winds and hunt. He is associated with the Vedic hymns and rituals, and is invoked for protection and healing. He is sometimes depicted as having multiple heads, eyes and arms, holding a bow, arrows, a trident and a drum.
Mahakala is the form of Shiva as the lord of time and death, the conqueror of all evils and the guardian of the directions. He is one of the most revered deities in Tibetan Buddhism, often depicted as a wrathful and terrifying figure, with a dark complexion, a third eye, a crown of skulls, a garland of severed heads, and various weapons and attributes.