Er-Gandalf Ghilir

Gandalf the White is an ancient Numenorian born on the ancestoral homeland of the Numenorians in the form of Atlantis, and he now serves the Kingdom of Gondor alongside his friend Aragorn Elessar.

Illumination
As Gandalf the Grey, Gandalf was not capable of very powerful spells, though he still had potency up to an extent. One of his simpler spells was illumination. In Moria, Gandalf was obliged to light his staff so that the Fellowship could find their way out of Moria. Because of the light provided by Gandalf's staff, the Fellowship was able to pass over many dangers and eventually find their way out of Moria.

Magical Kinesis
Gandalf the Grey was also capable of pushing his foes back with his staff, as shown in the movie when he battles Saruman in Orthanc. He tried to defeat Saruman as best as he could, but the White Wizard's power was too great for him to withstand. Eventually, Saruman stole Gandalf's staff and transported him to the top of Orthanc.

Call Gwaihir
When times grew desperate, Gandalf contacted Gwaihir, Lord of the Eagles, by means of a small moth. Gandalf had saved the great Eagle from a poisoned arrow long ago, and as a result, Gwaihir was eager and ready to help out his own friend whenever he needed to. Gandalf called Gwaihir multiple times, in places ranging from Orthanc to Moria to the Black Gate of Mordor. Though not so much a magical ability as an extra lifeline, Gandalf knew exactly when he needed help and when he should call Gwaihir to get it.

It was Radagast the Brown who told the eagles that Gandalf had visited with Saruman in the books; in the movie, Gandalf is seen speaking with the moth.

Sword of Power
In the film adaptation of The Two Towers, while Gandalf was facing the Balrog, he charged his sword Glamdring with lightning. He then struck his foe and killed him. It is unknown whether Gandalf actually summoned the lightning or simply attracted it toward Glamdring, but either way, his sword had extra power, enough to slay the Balrog of Morgoth.

Call Shadowfax
Although not magical as such, Gandalf develops a friendship with the "Lord of horses", Shadowfax in both the books and the films. After Gandalf takes Shadowfax from King Theoden's stables in Edoras, the horse develops a bond with Gandalf which meant that nobody else could ride or even touch Shadowfax, besides him. In the second film, Gandalf calls to Shadowfax by whistling just outside of Fangorn. Such is the bond between them that Gandalf rides Shadowfax without any harnesses and can direct him with his mind.

Stronger Magical Abilities
As Gandalf the White; Gandalf had amazing new powers and learned several skills and spells to defeat his foes. The skills listed below are those that either are completely new to Gandalf or have been significantly enhanced since his transformation from the Grey Wizard to the White Wizard.

Lightning Strike
This power is clearly described in the book The Hobbit in the Misty Mountains while escaping from an orc horde (obviously as Gandalf the Grey). He kills a few orcs and temporarily hides. The cartoon version of The Hobbit also boasts him using it during the Battle of Five Armies.

Blinding Light
Gandalf's second skill was Blinding Light, with which he would strike his foes blind with a blast of light resembling a magnified sunbeam. Though this particular attack did not deal much damage to foes in itself, it allowed any soldiers or cavalry to cut their enemies down with little to no resistance. Gandalf uses this spell once in the movies against the Fell Beasts of the Nazgûl so that Faramir's company could retreat to Minas Tirith safely. Gandalf did not use this Skill during the Battle of Helm's Deep, as is erroneously claimed, as the blinding light was caused by the rising Sun rising in the East ("On the morning of the fifth day, look to the East"). Blinding Light is quite possibly a much stronger version of Illumination.

Shield of the Istari
Gandalf can also conjure up a magical shield to protect himself from enemy attacks. It is shown in the movies only once, when Gandalf stands against the Balrog's flaming sword. However, on the extended version of The Return of the King, Gandalf uses the shield of Istari to protect himself from a spell cast by Saruman.

Fire
Gandalf uses the power of fire in the Hobbit, to light pinecones in multi-colored fire and to throw them at wolves; he also uses fire in the Fellowship of the Ring to cast ablaze a bundle of wood, and a large cluster of trees to stay warm, and to combat more wolves.

Destructive Blast
By far Gandalf's most devastating power is the destructive blast. Gandalf initiates this by raising his staff into the air and slamming it down on the ground. The weaker version is enough to break the Bridge of Khazad-dum, but at full power it can send surrounding legions flying into the air, instantly destroying them.