Shinto

Shinto (神道), or Shintoism is the indigenous religion of Japan. In Toaru Majutsu no Index, Shinto is used as a base for certain forms of Magic.

Principles
Essentially, it's a set of practices, to be carried out diligently, to establish a connection between present day Japan and its ancient past. Shinto today is a term that applies to public shrines suited to various purposes such as war memorials, harvest festivals, romance, and historical monuments, as well as various sectarian organizations. It's notable for being rather light on philosophizing and heavy on community spirits.

There are also splits over whether non-Japanese can practice Shinto/convert to it. This is heavily generalized and controversial since Shinto is not an evangelizing religion and is a practice faith. One faction insists they cannot (the nationalists, and traditionalists in general, say that you have to have Japanese blood to be "true" Shinto), another insists they can via marriage (e.g. some more open Shinto practitioners say that if a non-Japanese woman marries a Japanese man, or a non-Japanese man marries a Japanese woman-no one has spoken out regarding same-sex relationships yet-that the non-Japanese person is automatically "in" or alternately can choose to convert, similar to ethnic Judaism), and the most open faction welcomes and embraces non-Japanese and accepts the idea that while the belief system is non-evangelical and non-conversive, that someone may identify strongly with it or practice similarly to it.

Uses of Shinto in the story

 * Yomotsu-Shikome: A hag (or eight hags) sent by the dead Izanami after her husband Izanagi for breaking his promise in the land of the dead.
 * Marian Slingeneyer uses Dáinsleif to summon Yomotsu-Shikome by cutting away the Takama-ga-hara Phase.

Users of Shinto-related Magic

 * Amakusa-Style Remix of Church
 * Yamisaka Ouma