Every time I think "we" (the online Tolkien fannish community) may have a fairly complete catalog of all examples of magic in THE HOBBIT, THE LORD OF THE RINGS, and THE SILMARILLION, someone blows me away with a new list.

Someone further down in the thread suggested I might point you to my essay "Understanding Magic in J.R.R. Tolkien's Middle-earth". I'll provide the link below, but though the essay was written only this year after much thoughtful discussion here and in the Tolkien news groups, it barely scratches the surface of examples of we are calling "magic" in the books.

I wrote the essay to serve as a starting point for discussions of magic, not to be a definitive and exhaustive treatment of the subject. It reflects several points of view which I've now come to share as a result of reading what others had to say about magic in Middle-earth.

But the latest issue of the journal Other Hands has, I believe, the most complete catalog of magical phenomena ever put together in an article by Martin Burke titled "Magic in the Third Age". Burke's article is thorough and well-thought out, although I don't necessarily agree with everything he has to say. Nonetheless, he covered some issues that don't arise in my essay, and his methodology is considerably different from my own (he is providing a framework that gamers can use in their campaigns -- my treatment of the subject is much more theoretical).

I know that not everyone subscribes to Other Hands, but if you subscribe to other Tolkien journals you may want to encourage them to ask Chris Seeman (the publisher of Other Hands) for permission to reprint the article.

With respect to your specific question, I can easily recall the following "abilities" Gandalf demonstrated in the books. Keep in mind, however, that Gandalf was given new strength and new authority by Iluvatar, who sent his spirit back to Middle-earth after Gandalf died as a result of his combat with the Balrog:

1) He uses lightning (sometimes great bolts, sometimes little
flashes).

2) He is able to ignite his staff or any peace of wood or
burnable material into flame.

3) He can cause his staff tip to glow.

4) He can (apparently -- some people question this) enlarge
himself to giant size.

5) He can cause great destruction in stone structures, as
when he brought part of the mountain down on the Balrog
in the Chamber of Mazarbul (with the Word of Command) or
when he destroyed the bridge over the chasm in Moria.

6) He has some limited healing ability, although apparently
not enough to counteract the Black Breath of the Nazgul.

7) He use his mind to communicate with others. This may not
seem "magical" to some people.

8) He can struggle in a "contest of wills" (as when he was able
to persuade Frodo to take off the Ring while Sauron was
frantically trying to locate Frodo on Amon Hen). He also
seems to have overcome Saruman in a similar contest when
he commanded Saruman to return to him.

9) He can cause water to take on shapes of things, as when he
caused Elrond's flood to resemble the onset of white horses.

As has been pointed out by a couple of the others, Gandalf was able to use Narya to "kindle hearts" among Elves and Men (and apparently Hobbits and Dwarves). His inherent power was also enhanced by the Ring.

But I suspect Gandalf was capable of far more things than it was useful for Tolkien to put into the stories we have of him.

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Understanding Magic in J.R.R. Tolkien's Middle-earth