It's thought that Arab traders knew about Mauritius since at least the tenth century, but they never really stopped to colonize it the way they did with other places in the Indian Ocean. When Mauritius first appears on maps around 1500, it does so under the Arabic name Dina Arobi. The first Europeans to land on the island were Portugese. Domingo Fernandez Pereira came first somewhere around 1511, and he probably named the island Cirne, a name which apparently bore some relationship to the dodo birds that dominated the island at the time (although I'm sorry to say the exact nature of the relationship escapes me). The next European was Don Pedro Mascarenhas, who apparently hadn't heard anything about Pereira's landing and so renamed the island (along with its neighbors Runion and Rodrigues) the Mascarenes.
The Portugese apparently found Mauritius to be not to their liking, because they never went back after Mascarenhas' journey. This may have been because of the monkeys and rats they introduced to the island, although you'd have to ask them to find out for sure. In the absence of Portugal, Holland moved in on the island. A squadron of ships landed in 1598 under the orders of Admiral Wybrand Van Warwyck and claimed the place for Maurice of Nassau, then head of state for Holland, naming it Mauritius after him as well. After claiming it, the ships promptly weighed anchor and sailed off into the distance.
Forty years later, the Dutch figured they may as well colonize Mauritius as long as they own it, since it would be a useful stopping point on the way to Java. In 1638, Holland sent a group of colonists to Mauritius who brought with them sugar cane, domestic animals, wild boar and Javanese deer. As the latter found a foothold on the island, the Dutch colonists themselves failed to do so, although they didn't neglect to drive the dodo into extinction as long as they were there. The first settlement lasted twenty years but was abandoned in 1658. Again the Dutch sent colonists, and again the colonists were not up to the task. This cycle went on and on until the Dutch finally threw up their hands and stormed off Mauritius for the last time in 1710.
In 1715, Guillaume Dufresne D'Arsel landed a ship on Mauritius. Not finding anybody Dutch (or indeed, anybody at all other than the African slaves the Dutch had left), he experienced no pangs of regret when he claimed the island for France. Apparently taking note that Mauritius was an island and that it now belonged to France, he gave it the extremely accurate but not very creative name Isle de France. After a six year waiting period, France began to colonize the island in order to support the voyages of the French East India Company, who actually administered the island anyway. Things were kind of bumpy at first until in 1735 France brought in a high-powered management type, Governor Mahé de La Bourdonnais, to really get Mauritius going. He did a great job at it. He established Port Louis on the north side of the island, put in a hospital and road network, and a number of very nice buildings were also erected during his governorship. That may seem like an elementary accomplishment, but keep in mind that when there are 0 buildings to begin with, more than 0 buildings is an improvement of infinite percent.
The French East India Company gave up governing the island in 1767, leaving it to French government officials. Nothing really happened for a while, although during the French Revolution Mauritius was forced to set up an independent government until things settled down on the home front. Other than that, the next major change that took place in Mauritius was during the Napoleonic Wars. The Napoleonic Wars affected more of the world than really any other war until that time, and Mauritius was no exception. France used the island as a base for its corsairs to attack British merchant ships during the war, a fact which brought the wrath of the British down on Mauritius. First, a strong British force was sent in August 1810 from Rodrigues, which had already been captured by Britain. Although it was turned back at the Battle of Vieux Grand Port, its big brother that came to Mauritius in December was not so easily repelled. The British landed at the north of the island at Cap Malheureux and overwhelmed the French easily, taking control of the island. Mauritius was officially ceded to Britain by the Treaty of Paris in 1814.
Robert Farquhar was the first British governor of the island, and under his rule things changed rather drastically. First of all, the island was given its first Council of Government in 1825, which, although it didn't have popularly elected members until 1886, was still the first attempt at Mauritian sovereignty. Also, the French planters had been using slaves in their farming, so when it was outlawed in 1835 they had to take their two million compensatory pounds from the English government and figure out a new way to make sugar out of dirt. Mauritian society not only had to adjust to all the newly freed slaves but also had to adjust to the new workforce the planters brought in to replace them: indentured servants from India. Clearly, this changed the ethnic makeup of Mauritius substantially, and the community of small Chinese traders that grew up not too long thereafter diversified things as well. Economically, the island had great times in the years that followed. The export of sugar to England was the backbone of the economy, and England liked sugar. The economic progress that resulted allowed the country to build a good infrastructure and prosper.
Prosperity produced vastly wealthy European plantation owners, but didn't do much for the disenfranchised ethnic minorities who did all the actual work on the island. The Indians in particular, being the largest minority there, felt particularly underrepresented. It might be kind of silly to call the Indians a minority, since their main strength in their fight for representation was their pure numeric might. Mahatma Gandhi visited Mauritius in 1901 to lend his strength to the fight, and conditions gradually improved for the Mauritian Indians. The Labour Party, led by future English knight Dr. Seewoosagur Ramgoolam, was founded in 1936 to this end, and the next year suffrage was granted to anyone over 21 who could sign their name.
Mauritius was granted independence by Britain on March 12, 1968 and became a Commonwealth. Dr. Ramgoolam was elected their first prime minister and kept the job for 13 years thereafter. Following him was a government headed by a coalition of the two groups Mouvement Militant Mauricien (MMM) and the Parti Socialiste Mauricien. Top-level infighting made this administration slightly less stable, although nothing really terrible happened. The most interesting occurence was in 1986, when three Mauritian military policemen were caught with heroin in their suitcases at the Amsterdam airport. This was a big scandal for Mauritius, and several top officials resigned in the resulting brouhaha after being implicated in drug-related crimes.
Mauritius officially became a republic in 1992, three years before Navin Ramgoolam, grandson of the aformentioned elder Ramgoolam, took office as prime minister. Under his rule the country experienced the worst upheaval since the extinction of the dodos. In 1999, Joseph "Kaya" Topize was killed while in police custody. A reggae singer, he had been arrested at a rally to legalize marijuana and died of a skull fracture. Race riots between African creoles and Indo-Mauritians broke out in Port Louis, and to a lesser extent affected the rest of the island as well. This was the only time, except for the British takeover in 1810, that the general serenity of the island was severely disturbed. In the 2000 elections, Mauritians again decided to go with a coalition of groups as prime minister. The PSM's Anerood Jugnath will hold office until 2003, when the MMM's Paul Berenger, the first non-Hindu prime minister in Mauritian history, will take over.
Sources: http://ncb.intnet.mu/govt/history.htm,
http://www.lonelyplanet.com/destinations/africa/mauritius/history.htm
http://www.beachcomber.com.au/NewMauritius/history.htm