The 17 main types of magic are listed below:

Fire magic
Fire magic is a common tenet of magic used to control and/or summon fire.

Wind magic
Wind magic is a common tenet of magic used to control and/or summon wind and sometimes the air itself in other ways.

Sky magic
Sky magic is similar to Wind magic but is used to control the skies and stars themselves in addition to the earthly sky. A common example is star divination.

Earth magic
Earth magic is a common tenet of magic used to manipulate terrain and/or summon minerals.

Water magic
Water magic is a common tenet of magic used to control and/or summon water. Ice is sometimes seen as a subtype of this magic.

Ice magic
Ice magic is a common tenet of magic used to control and/or summon Ice and snow. Ice magic is sometimes seen as a subtype of water magic.

Light magic
Light magic is a common tenet of magic often used by "the good guy" but in actuallity has no pure alignment between good or evil.

Spirit magic
Spirit magic is a magic that can be used to control or otherwise contract with spirits and use their power. Spirit magic is sometimes seen as a subtype of light magic.

Summoning magic
Summoning magic is a magic that is used to "Summon"(Bring to thyself) a contracted person(s) or beast(s). This can range from tamed beasts like slimes and dragons to summoning Gods. This is sometime seen as a subclass of Space magic.

Nature magic
Nature magic is a type of magic used to control plants often trees. While it can also be used in combination to Summoning magic to summon nature fairies/dyrads it is most commonly used to control vines, trees, and flowers. 

Dark magic
Dark magic (Sometimes called "darkness" or "evil" magic) is a common tenet of magic often used by "the bad guy" or villian but in actuallity has no pure alignment between good or evil - Thought more morally ambiguous people are known to use this type. 

Soul(Life) magic
Soul magic, sometimes refered to as simply 'Life magic' is the magic that regulates life and death or more specifically the cycle of souls.

Creation magic
Creation magic is a magic used to create new matter and energy, sometimes seen as an ancient cousin of light magic creation magic is the power used to create the universe by the gods. Furthermore creation magic can only be used partially by mortals for basic elements unless such mortal is given a blessing by a god or goddess. Fire, Wind, Earth, Water, Ice, Light, and Dark magic are all seen as a subtype of a basic form of creation magic.

Destruction magic
Destruction magic is the counterpart of creation magic and can destroy anything at the cost of a great deal of mana. Destruction magic is the primordial ancestor or dark magic.

Mind influencing magic
Mind influencing magic is a morally dubious type of magic used to control or otherwise manipulate the mind(s) of other people(s).

Fate magic
Fate magic is the most primordial of magics and is incredibly hard to influence. Not much is known about this class of magic.

Space magic
Space magic, sometimes referred to as teleportation or warp magic is a magic used to transport something from one place to another commonly, however on a higher level space magic can be used to create and destroy universes. 

Time magic
Time magic is a complex magic no known mortal can accomplish that can stop and otherwise manipulate time.

Antimagic
Antimagic is often considered magic despite in-reality being the exact opposite. Antimagic is a subclass of Dark magic that counteracts the normal magic(s) if the world by cast a "Shadow" or exact opposite of a spell with dark magic to cancel the original.