Basic Research Understanding:
Some technologies are mutually exclusive. These are shown in yellow. You can only get one of the possible technologies. Example: Military Docks and Civilian Docks can't both be researched.
There is 1 group of technologies shown in red. These allow you to advance to the next tech level. Choose carefully. Once you chose one advancement track, you can never change.
To advance tech levels: Research "Research Lab" to level 1-5. This will enable 3 red technologies. Choose your path (Cyborg, Human [Brain], or Biological [DNA]). At level x-3 you will have access to the next tech level's items. The next tech level upgrade will be enabled once you reach x-5 of the current track and will be shown in yellow.
See the Tech Tree for research prerequisites.