The cerebral cortex was the part of the brain involved in many higher-level tasks such as language, memory, and consciousness. The cerebral cortex includes the parietal lobes, the occipital lobe, the frontal lobe, and the temporal lobes.
According to T'Pol the cerebral cortex was the most sophisticated computer known to exist. (ENT: "Dead Stop")
A burst of seventy millivolts would burn out the cerebral cortex of a normal humanoid brain. This, however, could be cheated with an injection of an inaprovaline drug, which provided additional resistance against such excessive electro-stimulation. (DS9: "Life Support")
Ceti eels from Ceti Alpha V entered through a humanoid's body by the ear and wrapped around the cerebral cortex, causing the victim to be susceptible to suggestion. (Star Trek II: The Wrath of Khan)
If damaged, tissue in the cerebral cortex could also be treated using a cortical analeptic. (VOY: "The Swarm")
When Deanna Troi temporarily lost her empathic sense due to the influence of two-dimensional beings in 2367, Dr. Crusher recorded a pattern of unresponsive neural cells in her cerebral cortex and cerebellum. (TNG: "The Loss")
In 2369, there was neuro-electrical activity in Joshua Kelly's cerebral cortex after his death due to the presence of quasi-energy microbes, giving the appearance he was alive. TNG: "Realm Of Fear")
Soon after, Crusher found abnormally high levels of neurotransmitter residue in Sev Maylor's cerebral cortex upon examination of her corpse. (TNG: "Man Of The People")
The Prytt used a psi-wave device implanted in the cerebral cortex as an interrogation method. (TNG: "Attached")
In an alternate 2372, Harry Kim suggested disproving Admiral Strickler's accusation of espionage by running a microcellular scan of his cerebral cortex to prove his memory had not been altered. (VOY: "Non Sequitur")
For a time, The Doctor's mobile emitter was located in One's cerebral cortex, adapted to serve as his central nervous system. (VOY: "Drone")
Seven of Nine's cerebral cortex underwent severe stress in 2375, when a malfunctioning Borg vinculum caused numerous neural patterns from assimilated individuals to overwhelm her mind. (VOY: "Infinite Regress")
Later that year, Seven detected unusual synaptic activity in Kim's cerebral cortex. This was as a result of the biochemical bond created with Derran Tal during their intimate relations. (VOY: "The Disease")
In TNG: "Violations", Crusher incorrectly identifies the thalamus as part of the cerebral cortex, when it is actually part of the brain stem.