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The following buildings can be constructed in a Campus:
At first, the main source of Science production comes from the Campus adjacency bonus. Due to its prevalence, 2 or 3 adjacent Mountain tiles for each Campus is most ideal. Rainforest tiles are not as good for general production but can be used to provide meaningful early Science boost through a well positioned Campus. (Towards very late game with Conservation civic in Modern Era, rainforests may be harvested and tiles converted to woods for lumber production.) Cities that provide such terrains should be where you build Campuses first. On the same token, it is advisable to seek out such terrains for planning "the science city". Economic Policy Natural Philosophy doubles the adjacency bonus. However, when Natural Philosophy becomes available, the number of Campuses is likely limited, which limits the effect of the policy; as a result Craftsmen is more likely to take the precious policy spot. Adjacency bonus could also serve as a guide for prioritizing among Campus, Industrial Zone, Commercial Hub or Harbor, and Holy Site (of which you only need one early game unless you are pursuing a faith purchase strategy).
At early game, any city-state bonus on Science will be massive. Therefore, Science city-state are much sought after early game. This puts heavy emphasis on early game scouting. The first of any science city-state bonus provides a net +2 nationwide. The second and the third bonuses are +2 every Campus. This can be further assisted by Founder Belief Papal Primacy, which you may select if you happen to run into a Science city-state nearby early. The second bonus is most attainable early game. You may obtain 1 free Influence Points from first contact or from Diplomatic League policy. You may also obtain another free Influence Point from fulfilling the city-state mission. Therefore, the 3 Influence Points can be obtained with only 1 or 2 Envoy. 1 Envoy would be luck based. However, 2 Envoy is perfectly under player control. (Note that the city-state bonus will apply to Campus districts. Therefore you must build some Campuses in order to take advantage of Science city-states. So the planning of Campus building can be independent of city-state discovery.)
Later, after University becomes available in Medieval era, the Science production from Campus buildings become predominate. This is especially true starting in Renaissance era with Rationalism, which doubles the Campus building outputs. You are most likely to maintain Rationalism policy from the moment it becomes available until very late game. Therefore, one may as well think of the +1 from Library as +2 and +4 from University as +8 . Together, we see that the +10 from specialty buildings starts to overtake adjacency bonus and city-state bonus. This puts emphasis on constructing Universities early and enabling Rationalism policy early. Both Rationalism and city-state bonuses award on number of campus. Therefore, go-wide strategy is better for Science than go-tall (as with all other resource production). Into mid-game, cities that do not sport high adjacency bonus for Campus districts should also start to construct Campuses unless you are receiving significant boosts from city-states and Great Scientists.
Great Scientist Albert Einstein doubles the Science output of all Universities (+4). This is the most overpowered Great Scientist, followed by Isaac Newton, who increases the Science output of all Universities by half (+2). Remember that the true bonus is always doubled with Rationalism policy. Therefore, the bonuses of these two Great Scientists are massive. It is worth fighting for a Science lead, which induces a Great Scientist point lead. While a lead in Great Scientist point does not guarantee access of the Great Scientist of choice, it greatly increases the chance of obtaining a better Great Scientist. To the contrary, trailing behind in Great Scientist point greatly reduces the chance of obtaining a good Great Scientist, especially in multiplayer games. Having Albert Einstein greatly reduces the pressure of having many campuses. This is where the surprise effect of RNG comes in to be fun.
The term "campus" is the Latin word for "field," and was first applied to the grounds of what would become Princeton University founded in 1746 AD; the word has since come to be applied to the usually landscaped setting of any institution of higher learning (and, sometimes, to pretentious corporate office complexes). The tradition of the campus as a special district devoted to learning has its roots in 12th century European schools where instructors and students lived together in a self-regulating, cloistered settlement. Those early campuses with their collective rights and legal privileges were often guaranteed by charters from princes or prelates, with the land "donated" by the town in which they were located.