The Mage's Guild is one of the main guilds of Morrowind. It offers training in the various schools of magic, supplies and services for the adventuring mage. Through preforming duties and meeting various skill level requirements you can advance through the ranks of the Mage's Guild to become an Archmage and get access to the best services and training.
There are five Mage's guild locations in Morrowind. The first one a player will come across is the one in Balmora. The other guilds are located in Aid'Ruhn, Caldera, Wolverine Hall in Sadrith Mora, and Vivec.
Many different people within the Mage's guild can train you in the various schools of magic. You can find training for all schools though within every Mage's guild. The various schools of magic such as Restoration, Mysticism, Alteration, Destruction. Illusion, and Conjuration. Among these things other training is offered based on who you ask. Training costs a certain amount of gold and increases as your skill becomes higher. Certain people within the guild can only train you as high as their skill allows them, so eventually you will have to find masters of those skills in order to train.
Many services are available at the Mage's Guild. These services include bartering with other mages for potions, scrolls, and other magical items such as soul gems. Other services also include purchasing spells from all the schools of magic and making spells of your own. Unique to the Mage's Guild is the service of paying gold to be teleported to the other Mage's Guild locations which can speed up travel and allow quick completion of interguild quests.