Sid Meier's Civilization V/Technologies

Technologies are one of the major aspects of the game, as they indirectly affect how advanced you are in other aspects in the game. It also plays a key role in obtaining a Scientific Victory. Technologies require science to produce, which is rounded off into the number of turns needed. Changing the game speed will also change the cost of each tech, so the science cost displayed below only applies for the Standard game speed.

Agriculture
Agriculture played a key role in creating the earliest human civilizations. It allowed humans to abandon a nomadic lifestyle and settle down due to the ability to maintain a reliable and lasting source of food. Quite fittingly, it is the technology you start with in the Ancient Era, and gives you the ability to create the Farm tile improvement, useful for providing more food to your population.
 * Cost: 20
 * Leads to: Pottery, Animal Husbandry, Archery and Mining.
 * Enables Farm

Pottery
Pottery is perhaps one of the oldest forms of art. By shaping clay and heating it, ancient humans could create brittle but useful containers. It opens up a bunch of new research possibilities as well as gives you two helpful buildings. The Granary is useful for early growth while the Shrine is an early source of faith.
 * Cost: 35
 * Prerequisites: Agriculture
 * Leads to: Sailing, Calendar, Writing
 * Enables Granary, Shrine (G&K)

Animal Husbandry
Animal Husbandry is the act of domesticating animals, either for food or utility. It reveals horses, a major strategic resource used throughout the Classical to Renaissance Eras, that let you create mounted military units.
 * Cost: 35
 * Prerequisites: Agriculture
 * Leads to: Trapping, The Wheel
 * Reveals Horses, enables Pasture

Archery
Archery involves the use of a bow to launch a thin projectile, a skill used for hunting and for most wars before the discovery of gunpowder. It lets you train the earliest ranged units, the Archers, which can be used to defend your cities and pepper barbarians.
 * Cost: 35
 * Prerequisites: Agriculture
 * Leads to: Mathematics
 * Enables Archers and Temple of Artemis

Mining
Mining is the act of excavating and extracting useful elements and minerals from the earth. It lets you contruct mines and clear forests, both of which gives you boosts in production. Mines are also needed to take advantage of a bunch of strategic and luxury resources, from Salt to Uranium, though you won't be able to do that until later in the game.
 * Cost: 35
 * Prerequisites: Agriculture
 * Leads to: Masonry, Bronze Working
 * Enables Mines and the ability to clear forests

Sailing

 * Cost: 55
 * Prerequisites: Pottery
 * Leads to: Optics
 * Enables Work Boats, Triremes, Great Lighthouse and Fishing Boats

Calendar

 * Cost: 55
 * Prerequisites: Pottery
 * Leads to: Theology
 * Enables Stonehenge, Stone Works and Plantations

Writing

 * Cost: 55
 * Prerequisites: Pottery
 * Leads to: Philosophy
 * Enables Library, Great Library and Open Borders

Trapping

 * Cost: 55
 * Prerequisites: Animal Husbandry
 * Leads to: Civil Service
 * Enables Circus, Trading Post and Camps

The Wheel

 * Cost: 55
 * Prerequisites: Animal Husbandry
 * Leads to: Horseback Riding and Mathematics
 * Enables Chariot Archers, Water Mill and Roads

Masonry

 * Cost: 55
 * Prerequisites: Mining
 * Leads to: Construction
 * Enables Walls, Pyramids, Quarries and lets you clear marshes

Bronze Working

 * Cost: 55
 * Prerequisites: Mining
 * Leads to: Iron Working
 * Enables Spearmen, Barracks, Statue of Zeus and lets you cut down forests

Optics

 * Cost: 80
 * Prerequisites: Sailing
 * Leads to: Compass
 * Enables Lighthouse and embarking

Philosophy

 * Cost: 100
 * Prerequisites: Writing
 * Leads to: Theology and Civil Service
 * Enables Temples, National College, National Epic, The Oracle and Research Agreement

Horse Riding

 * Cost: 100
 * Prerequisites: The Wheel
 * Leads to: Chivalry
 * Enables Horsemen and Stables

Mathematics

 * Cost: 100
 * Prerequisites: The Wheel, Archery
 * Leads to: Currency and Engineering
 * Enables Catapults, Courthouses and Hanging Gardens

Construction

 * Cost: 100
 * Prerequisites: Masonry
 * Leads to: Engineering
 * Enables Composite Bowman (G&K), Colosseum, Circus Maximus, The Great Wall and Lumber Mills

Iron Working

 * Cost: 150
 * Prerequisites: Bronze Working
 * Leads to: Metal Casting
 * Enables Swordmen, Heroic Epic and reveals Iron resources.