Here's a try at a brief history of the war:
1702: May 15: War declared. France, Spain, and Savoy against England, the Netherlands, Austria, and Baden. Portugal had signed an alliance with France and Spain, but wasn't actively participating. Bavaria was inclining towards the French.
In Italy, Prince Eugene of Savoy led the outnumbered Austrian forces against the French and Spanish under Vendome. Marlborough led an Anglo-Dutch force and although obstructed by the Dutch deputies was able to expel the French from the Maas and lower Rhine.
Admiral Rooke led an Anglo-Dutch force in an attempt to seize Cadiz, which ended in fiasco. However, on the way home, Rooke attacked Vigo destroying the Plate fleet and 15 French ships of the line.
In September, Bavaria joined France with the understanding that it would get greatly increased territories and the Imperial throne after victory had been acheived.
1703:Marlborough invaded the Electorate of Cologne and catpured Bonn. He then returned to the Netherlands, where his plans were ruined by the antagonism of the Dutch generals.
A French army advanced through Baden and, after linking with the Elector of Bavaria's army, moved into the Tyrol. Vienna was menaced by Hungarian insurgents and by the end of the year, Austria was in a desperate position. Eugene was recalled from Italy by Emperor Leopold.
In May, Portugal defected from France and signed an alliance with England. In October, Savoy, increasingly distrustful of the French, allied with Austria.
1704: To prevent Austria from being defeated, Marlborough took his army into Germany against the protests of the Dutch. After moving into Bavaria, Marlborough encountered and routed a French force at Donauworth, losing 1,400 killed and 3,800 wounded to 10,000 total for the French. In August, Marlborough connected with Eugene and then attacked the main Franco-Bavarian army at Blenheim. Although outnumbered 52,000 to 60,000, the allies won a major victory, suffering 12,000 casualties while the French and Bavarians lost about 2/3rds of their army from casualties, prisoners, and desertions. This battle saved Austria and put France on the defensive for the rest of the war.
Also in this year, a force under Admiral Rooke captured Gibraltar from Spain and gained control of the Mediterranean.
1706: Marlborough won a victory over the French at Ramillies, forcing them to withdraw from the Netherlands. The French were also driven out of Italy.
1707: An Anglo-Portuguese force invaded Spain, but suffered defeat. Louis XIV's grandson, Philip V, retained control over most of the country.
1708: Marlborough won another victory at Oudenarde, causing Louis XIV to seek peace. However, the allies demanded that he help remove his grandson from power, causing negotiations to break down.
1709: Marlborough won his fourth great victory at Malplaquet, causing negotiations to resume, but break down for the same reason as before.
1711: Emperor Joseph died and his younger brother, who was to have inherited the Spanish throne, became Emperor Charles VI. Britain then worried about the Hapsburgs becoming predominant, leading the breakup of the Grand Alliance.
Peace negotiations began in 1712, leading to the Treaty of Utrecht in 1713 that established peace between France, on the one hand, and Britain, the Netherlands, Portugal, Savoy, and Prussia on the other. Austria attempted to continue alone, but ultimately made peace with France in 1714 and Spain in 1715.
