George Hamilton Feeny was Cory's sixth grade teacher (later retconned to being Cory's teacher from first grade. and then retconned again into being his teacher from sixth grade) as well as the neighbor of the Matthews family.
As the series progresses, he starts working in the John Adams High School, just when the main characters begin to attend there. Eventually, he becomes the principal, and later on a college professor at Pennbrook. From the start of the series, Feeny attempts to be strictly a teacher to his students, but later develops close relationships with Cory, Shawn, Topanga, and especially Eric.
When he is not teaching, Feeny is frequently spending time working in his garden, and his absence often shocks the Matthews. The family has gotten used to being able to talk to Feeny about anything, and getting valuable advice in return. Similarly, Feeny seems stressed when he knows something important has occurred, yet no one has come to him for any advice, as seen in Raging Cory. Feeny acts like more the authority figure than a mentor.
Continued being the teacher of Cory & co., but gained some respect from them (especially in Life Lessons).
Went to Boston to meet an old flame, and Eric happened to be there. That is where their friendship seemed to be cemented.
Gradually became a friend and mentor of Cory, Shawn, Topanga, and Eric. He also had good relationships with Angela, Jack, and Rachel but he was especially close to the first four aforementioned students as he had known them the longest.
Planned to retire after everyone graduated, but Cory followed him and he decided to study at Pennbrook instead.
His teaching instincts took over, and he quickly became a professor at the college instead.