Oligarchy is a form of government that is available after completing the Political Philosophy civic. It offers the most well-rounded card selection available during the Classical era, as well as a major boost to early-game 
combat strength.
Strategy
For civilizations such as Greece under Gorgo, using Oligarchy is almost a given. Other civilizations whose leader bonuses deal with combat strength, such as Tomyris' Scythia, can also make great use of Oligarchy's strength bonus if played correctly. Even America, historically known as a mid-to-late game civilization, can use this government type to launch devastating early wars with a collective total of +9 combat strength while utilizing Oligarchy's legacy bonus in record time. Overall, Oligarchy makes for an extremely well-rounded government style for the Classical era.
Civilopedia Entry
Like all of civilization’s important words, the Greeks coined the term “oligarchy” to mean “ruled by the few.” Whether distinguished from the hoi polloi by family ties, religious or military prestige, personal achievements, or other attributes – Aristotle used the term to refer to rule by the rich, and Plato in The Republic argued for rule by an educated elite – the oligarchs determine what issues should be on the political agenda, debate these, and then decide “for the good of the people.” Depending on the qualifications imposed to be an oligarch, oligarchy is a fairly efficient form of government; although it does have an unfortunate tendency to become tyrannical.
Not surprisingly, the most notable oligarchies in history are found in ancient Greece – Corinth, Sparta, Thebes, in fact all the major city-states… except the democratic Athenians. However, recent works by political scholars such as the German sociologist Robert Michels argue there is an “Iron Law of Oligarchy” whereby all forms of government tend inevitably towards oligarchy. Even in representative democracies, the practical demands of governance results in the concentration of political power in a small group, in a monolithic bureaucracy, and in rigorous means to control dissention. Which may be a good thing, as the historian Spencer Weart claims that oligarchies rarely make war on each other.