The uses of magic span a wide range of learned abilities, natural talents, and preferences. From the natural chaos that is magic, the Circles of Magi attempted to make order, the better with to teach new generations of mages in an easy, standardized way.
There are four main schools of magic, but they aren't all encompassing. There is the Primal school, which is the magic of natural forces such as fire, frost, and lightning. The school of Spirit focuses on the raw energies of the Fade itself, and the energies commanded and purified by the spirits which live there. The school of Creation manipulates the various life forces of this world, transforming what exists and bringing new things into being. The fourth school is that of Entropy, which encompasses the magics of decay and inevitable destruction.
However, not even all the traditions of magic taught by the Circles fit into these four neat schools. Attempts are made, such as how many older Circle texts describe Force magic as an intersection of Spirit and Primal magic, but such an explanation falls quite short. Thus, it is more accurate to say these are other schools of specific magics.
Force magic is the study of using raw magical energy to manipulate objects of the physical world, to push, pull, and strike with magic. Spirit Healing is an extremely in-depth study of arts both magical and mundane, giving practitioners an unparalleled understanding of the physical body and the ability to work with spirits to heal it. Arcane magic is the base understanding of magical forces upon which all other traditions of magic are built.
There are even yet more traditions of magic, but most of the rest are specific to particular groups or locations of Thedas. It is difficult to learn anything of the specifics of such traditions, as their practitioners generally keep them from outsiders. The tradition of necromancy, passed from the masters of the Nevarran Mortalitasi to their apprentices, is the art of summoning spirits and wisps into the dead, breathing a shoddy semblance of life into an abandoned corpse. The enigmatic Dalish Keepers, leaders of their clans, are said to practice magics which allow them to physically control plants and the earth. There are accounts of Rivaini eirafat merging with spirits to predict the future, and Avvar augurs communing with spirits to guide and educate their peoples. Orth taikureita are said to command spirits to protect their clans from the ever-present threat of darkspawn, and Chasind wilderfolk tell stories of their own witches shapeshifting into other creatures, to spy on other tribes and on outsiders.
Finally, the practice of blood magic deserves but a brief mention. While many practitioners of this forbidden art claim to only use their own blood to power more permitted magics, the true dangers of blood magic lie in the spells which can only be cast in blood. The ability to summon demons unchecked, to control the minds and bodies of others, and commit other unspeakable acts of violence are quite unique to blood magic, and are the main reason it is forbidden. The other reason, of course, being that the use of such dark power draws demons near to the user, putting them in greater danger of corruption and possession.