Major Sections of Hinduism

Shaivism

 Shaivism is one of the four major sects of Hinduism, the others being Vaishnavism, Shaktism and the Smarta Tradition. Followers of Shaivism, called "Shaivas", revere Shiva as the Supreme Being. Shaivas believe that Shiva is All and in all, the creator, preserver, destroyer, revealer and concealer of all that is. He is not only the creator in Shaivism, but he is also the creation that results from him, he is everything and everywhere. Shiva is the primal soul, the pure consciousness and Absolute Reality in the Shaiva traditions.

The Shaivism theology is broadly grouped into two: the popular theology influenced by Shiva-Rudra in the Vedas, Epics and the Puranas; and the esoteric theology influenced by the Shiva and Shakti-related Tantra texts.The Vedic-Brahmanic Shiva theology includes both monist (Advaita) and devotional traditions (Dvaita) such as Tamil Shaiva Sidhanta and Lingaytism with temples featuring items such as linga, Shiva-Parvati iconography, bull Nandi within the premises, relief artwork showing mythologies and aspects of Shiva.

Tantric Shiva Shakti

The Tantric Shiva tradition ignored the mythologies and Puranas related to Shiva, and depending on the sub-school developed a spectrum of practices. For example, historical records suggest the tantric Kapalikas (literally, the "skull-men") co-existed with and shared many Vajrayana Buddhist rituals, engaged in esoteric practices that revered Shiva and Shakti wearing skulls, begged with empty skulls, used meat, alcohol, and sexuality as a part of ritual. In contrast, the esoteric tradition within Kashmir Shaivism has featured the Krama and Trika sub-traditions. The Krama sub-tradition focussed on esoteric rituals around Shiva-Kali pair. The Trika sub-tradition developed a theology of triads involving Shiva, combined it with an ascetic lifestyle focusing on personal Shiva in the pursuit of monistic self liberation.

Vaishnavism

The Vaishnava (Vishnu-oriented) literature acknowledges and discusses Shiva. Like Shaiva literature that presents Shiva as supreme, the Vaishnava literature presents Vishnu as supreme. However, both traditions are pluralistic and revere both Shiva and Vishnu (along with Devi), their texts do not show exclusivism, and Vaishnava texts such as the Bhagavata Purana while praising Krishna as the Ultimate Reality, also present Shiva and Shakti as a personalized form an equivalent to the same Ultimate Reality. The texts of Shaivism tradition similarly praise Vishnu. The Skanda Purana, for example, states:

Vishnu is nobody but Shiva, and he who is called Shiva is but identical with Vishnu.

— Skanda Purana, 1.8.20–21

Mythologies of both traditions include legends about who is superior, about Shiva paying homage to Vishnu, and Vishnu paying homage to Shiva. However, in texts and artwork of either tradition, the mutual salutes are symbolism for complementarity. The Mahabharata declares the unchanging Ultimate Reality (Brahman) to be identical to Shiva and to Vishnu, that Vishnu is the highest manifestation of Shiva, and Shiva is the highest manifestation of Vishnu.

Shaktism

Ardhanarishvara sculpture, Khajuraho, depicting Shiva with goddess Parvati as his equal half.

The goddess-oriented Shakti tradition of Hinduism is based on the premise that the Supreme Principle and the Ultimate Reality called Brahman is female (Devi), but it treats the male as her equal and complementary partner. This partner is Shiva.

The earliest evidence of the tradition of reverence for the feminine with Rudra-Shiva context, is found in the Hindu scripture Rigveda, in a hymn called the Devi Sukta:

I am the Queen, the gatherer-up of treasures, most thoughtful, first of those who merit worship.
     Thus gods have established me in many places with many homes to enter and abide in.
Through me alone all eat the food that feeds them, – each man who sees, breathes, hears the word outspoken.
     They know it not, yet I reside in the essence of the Universe. Hear, one and all, the truth as I declare it.

I, verily, myself announce and utter the word that gods and men alike shall welcome.
     I make the man I love exceeding mighty, make him nourished, a sage, and one who knows Brahman.
I bend the bow for Rudra [Shiva], that his arrow may strike, and slay the hater of devotion.
     I rouse and order battle for the people, I created Earth and Heaven and reside as their Inner Controller.
(...)

— Devi Sukta, Rigveda 10.125.3 – 10.125.8, 

The Devi Upanishad in its explanation of the theology of Shaktism, mentions and praises Shiva such as in its verse 19.Shiva, along with Vishnu, is a revered god in the Devi Mahatmya, a text of Shaktism considered by the tradition to be as important as the Bhagvad. The Ardhanariswara concept co-mingles god Shiva and goddess Shakti by presenting an icon that is half man and half woman, a representation and theme of union found in many Hindu texts and temples. 

Smarta Tradition 

Oleograph by Raja Ravi Varma depicting a Shiva-centric Panchayatana. A bearded Shiva sits in the centre with his wife Parvati and their infant son Ganesha; surrounded by (clockwise from left upper corner) Ganesha, Devi, Vishnu, and Surya. Shiva's mount is the bull Nandi below Shiva.

In the smarta Tradition of Hinduism, Shiva is a part of its Panchayatana Puja. This practice consists of the use of icons or anicons of five deities considered equivalent, set in a quincunx pattern. Shiva is one of the five deities, others being Vishnu, Devi (such as Parvati), Surya and Ganesha or Skanda or any personal god of devotee's preference (Ishta Devta).

Philosophically, the Smarta tradition emphasizes that all idols (murti) are icons to help focus on and visualize aspects of Brahman, rather than distinct beings. The ultimate goal in this practice is to transition past the use of icons, recognize the Absolute symbolized by the icons, on the path to realizing the nondual identity of one's Atman (soul, self) and the Brahman. Popularized by Adi Shankara, many Panchayatana mandalas and temples have been uncovered that are from the Gupta period, and one Panchayatana set from the village of Nand (about 24 kilometers from Ajmer) has been dated to belong to the Kushan Empire era (pre-300 CE). The Kushan period set includes Shiva, Vishnu, Surya, Brahma and one deity whose identity is unclear.