The Hymn to Shiva are quite a few, however most popular of these are following.

First one is the Shiva mantra 'Aum Namaḥ Śivāya', Its short and easy to remember and hence is used as a prayer for Lord Shiva by most of the Hindus.

Second one is a bit long, it's titled as the Shiv Tandav Stotram. It is a prayer written by the Rakshasa King Ravana in the praise of Lord Shiva. You can find a youtube link to the Tandava Stotra in related links.

Even though 'Aum Namaḥ Śivāya' is a short mantra and cannot be sung as a prayer however it still fulfills the specifications of a hymn and can be considered as a hymn.

Tāṇḍava or Tāṇḍava nṛtya, the divine art form, is a dance performed by the god Shiva, who is revered by Hindus.

In the Hindu texts, at least seven types of Tandava are found:

• Ananda Tandava

• Tripura Tandava

• Sandhya Tandava

• Samhara Tandava

• Kali (Kalika) Tandava

• Uma Tandava

• Gauri Tandava

In Bharata Natyam, the national dance of India - The symbolism of the dance of Shiva (in the form of Nataraja) is represented by the attitude called "Ananda Tandavam"

While the Rudra Tandava depicts Lord Shiva's violent nature, first as the creator and later as the destroyer of the universe, even of death itself; the Ananda Tandava depicts him as the enjoyer of his creation - the universe.