Advanced genetics is the study of genetics on a more complex level.
In 2366, Wesley Crusher was working on nanotechnology as part of his advanced genetics project. He studied nanites with the theory that by working together, they could combine their skills and increase their usefulness. However, his science experiment got out of hand when a nanite escaped its confinement in the science lab and began replicating on the USS Enterprise-D. The replicated nanites became intelligent and were the cause of several systems malfunctions all over the ship. (TNG: "Evolution")