The collective name for the group of technologies which are required for construction of buildings, ships and defenses is Research. New technologies are researched in a planet’s Research Lab. Each technology has certain prerequisites - a certain level of Research Lab and, possibly, one or more other technologies. Thereafter the only requirement is the cost (availability of resources). The resource cost to research each level of a given technology is twice that of the previous level [excluding Astrophysics, which is 1.75x with the result being rounded to the nearest multiple of 100, and Graviton Technology, for which each level triples in cost].
The time taken to research a new level of technology depends on the amount of metal and crystal that particular level costs (more expensive levels take longer to research). Research times can be reduced by the level of the planet’s Research Lab, and even more with each level of Intergalactic Research Network, which combines Research Lab levels on multiple planets.
Hint: Some research projects are expensive, so you can prevent a large amount resources from being plundered by spending on a research project if you are attacked. Unlike buildings, however, research projects cannot be cancelled. Any resources spent on research cannot be reclaimed. Additionally, the time required for some research can be lengthy, so be sure to consider this before beginning the research. You cannot enter Vacation Mode until the research has completed.
See the Technology Tree for a list of requirements to research each technology.