Well, lets see:
Beam Weapons - pretty obvious, blasters and such. Torpedo Weapons - includes regular torpedoes and planetary bombardment torpedoes. Area Weapons - includes hyperdeny (prevents enemy ships from warping off) and AoE (area of effect) weapons. Armor - umm armor and better versions of same. Shields - umm shields and better versions of same. Engine - includes regular subwarp engines and maneuvering thrusters. HyperDrive - faster and/or more efficient warp engines. Reactor - better and/or more efficient power generation for ships and bases. [can require different fuel types] Energy Collector - extra, subsidiary solar cells for power generation of a stationary base/ship. Extractor - better mine engines (for non-gaseous objects), gas extractors and luxury extractors. Manufacturer - better production plants for construction ships and spaceports that allow more components of various types to be built faster. Storage - more efficient fuel cells, cargo bays, passenger compartments, troop compartments and docking bays. Sensor - better resource sensors (for your exploration ships), proximity sensors (for everything), long range scanners and cloaks. Computer - better command centers (maintenance reduction), commerce centers (trade bonus), ECM and Combat Sensors (to-hit bonus). Labs - better research centers for the 4 different research groupings. Construction - better shipyards that allow you to build bigger ships and bases. Habitation - better life support, hab modules, better colonization modules (other planet types), recreation centers, hospitals + damage reduction/repair.
Beam Weapons, Torpedo Weapons, Area Weapons and Armor are grouped under "W" or Weapons Research. Shields, Engine, HyperDrive, Reactor and Energy Collector are grouped under "E" or Energy Research. Extractor, Manufacturer, Storage and Construction are grouped under "I" or Industrial Research. Sensor, Computer, Labs and Habitation are grouped under "HT" or HighTech Research.