Research concept
Research plays a very important role in Projekt "W", as it unlocks new technologies, buildings, military units and upgrades existing parts of the game. So it's always a good idea to hire some scientists, construct some scientific buildings and start researching.

Research is done via the research window, with each technology requiring a certain number of turns to be finished. This number depends on your research factor, either the civil or military factor.

Once you've researched all basic technologies, infinite research will be unlocked making your scientific equipment useful, even after researching everything.
Research categories
There are three different categories of research in the game, each with it's own factor that influences how fast you can unlock the corresponding technologies and with it's own set of unlockable technologies :
Civil research
The technologies in this category usually unlock new buildings that affect your regions. Researching these is crucial for updating your old buildings to newer ones.
Military research
These technologies unlock new military units or enhance existing ones by e.g. upping their defense, adding static shields, etc. So if you want to win the war, researching these is a must.
Infinite resarch
Once you have researched all technologies, a new branch of the technology tree will open up, the infinite technologies. These were introduced to keep your scientists and scientific buildings useful, even after finishing all normal technologies. As long as one of these technologies is active it's effects are active, with the strength of the effect determinted by your research factors.
Research factors
There is a separate research factor for each of the two different areas. When you start a new game, both factors will be zero, which means that research on a selected technology will never be finished.

So before starting research you need to increase the research factor somehow. There are two ways of doing this, by either hiring scientists on the transfer market or constructing scientific buildings inside your regions. As for the buildings you can either construct those that only affect one factor (as they're a bit cheaper) or generalized scientific faculties that increase both factors.

Note : There is a cap on the research factors, so after a certain point constructing new buildings or hiring new staff won't increase the factors anymore. This cap is split between staff and buildings, so you'll never be able to reach this limit by only hiring scientists or only constructing buildings.

If you've started research progress will be shown in the lower left corner of the screen, so you can always check how many turns are left until the current technology will be finished :
Finishing research
Researching technologies is a passive task. So as long as your corresponding research factor is higher than zero, research on the selected technology will advance after ending your turn.

If progress is complete than the new technology will be unlocked and you'll be notified after ending your turn via a separate screen that tells you about it and also displays all unlocks of this technology.