He is the only character who is a principal figure throughout the whole book and undergoes a psychological change. He is also the one who ties up the disparate elements of the work.
At first he is shown as a young student just arrived from the provinces, full of dreams, prepared to work hard to become a successful lawyer. Of an aristocratic family, he has some influential relatives in Paris, and he is quick to realize that with their help he will enter one of the most restricted and brilliant circles in Paris. Fascinated by that luxury, by that life of pleasure, he wants to become a part of it. But to join a club, one has to follow the rules, and Eugene discovers that to become a member, he will have to leave behind some of his moral principles. He will have to cheat, to lie, to dull his sensibilities. He also realizes that the important instrument of success is money, the almighty god.
He first tries to compromise. Why not combine hard work and pleasure? But Vautrin is right at his side to whisper that hard work will lead him to a life of bourgeois mediocrity and that in the meantime he will need money.
Eugène is defeated, and although he argues with himself and feels remorse, he will exploit his mother and sisters, forget his studies, and when his money runs out, he finds himself lost, so lost that he will listen to Vautrin's criminal plot.
Little by little, he makes more and more concessions. He accepts his illicit liaison with Delphine, Goriot's money, his mistress' present. And by the end of the hook, he has definitely joined the club and will successfully abide by its rules.
In spite of all this, Eugène remains a sympathetic character because of his candor, his childish naïveté, and his love and devotion for Old Goriot.