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Sohma Yuki
Yuki is very quiet and withdrawn, although he is beginning to feel more comfortable with himself at this point in the series. Though his introverted nature In the manga, he often described himself as someone who kept his thoughts and feelings trapped under "a tightly sealed lid," and this is understandable since he's spent his entire life in confinement of one type or another.
Shy to begin with, Yuki was deliberately kept isolated from other children by the Sohmas because of the curse, and later by Akito as she took out her own frustrations on him, through physical and mental torture. Yuki's parents used him quite selfishly and kept themselves distant from him, discouraging him from turning to them for help or expressing his thoughts and feelings to them.
Yuki spent his childhood being told in words and actions that his life was hopeless, and that he was a means to an end and nothing else. As a result of his natural personality and his physical and emotional isolation, he has trouble making friends, and he is often very critical and contemptuous of himself as a person, and inferiority complex. He believes that others must accept and like you before you can like yourself, and Tohru has gone a long way to help him begin to see himself through her eyes. Hatsuharu also seems to have an unconditional fondness for Yuki, and Ayame is trying his best to reach out to him as well.
He is also extremely polite, always using the formal Japanese language, even calling Tohru as 'Honda-san' instead by her name. But he gets extremely happy when Tohru calls him for the first time by his first name, even he accidentally turned into his juunishi form.
Yuki confesses Tohru he acts kind to attract people, knowing that will help him to make friends and be accepted, though he regretfully admits his mannerism as not genuine, and feels miserable for it, even when a girl complains to him why he is so 'unreachable'. Yuki question himself how ironic is the fact he is accepted by the juunishi and the Sohmas, but not by 'normal' people, unlike Kyo who is excluded from the family yet accepted by their classmates, seen playing cards with them.

His past...
Yuki Sohma is the rat of the zodiac. Kind at heart, and a gentlemen at large, he attends Kaibara High School where he is regarded as a "Prince", a group of obsessive fangirls spy on him, follow him around, Yuki is aware of their presence, but treats them with apathy.
He suffers from insecurity, and also, claustrophobia. This is because, when he was young, the Head of the Zodiac-Kami-sama, Akito- would lock him in a tiny dark room, and whisper him things he could never forget. As the legend of the Juunishi tells, the rat was the first one to arrive to the god's banquet, therefore Akito considered him the closest, his plaything. Through cruelty, he sought to immortalize himself in the juunishi's memories. Yuki fears Akito, his uneasiness and anxiety clear in his presence, and Akito seems to enjoy that effect upon him. He does not trust him either, always suspects of what is Akito ultimately planning, though he treats him with respect. But as time passes he obtains enough confidence to defy Akito's wish to be assist to the New Year's celebration. Yuki secretly wishes to be 'freed' from the Sohma family, to him it has become a cage.
He is Ayame's younger brother, Yuki is ten years younger. Though their relationship is not exactly fraternal. At young age, Yuki needed him, the comforting company of a brother, but Ayame simply slapped his hand away and turned back leaving him alone. Later on, Ayame recognizes his mistakes and attempts to mend their relationship, but Yuki explains their way of thinking is too different. He is often embarrassed by Ayame's boastful and perverted remarks. Even he fails to understand the meaning of Ayame's 'special' store.
Kyo, the cat, is his rival. He challenges Yuki regularly, constantly seeking to defeat him. But most of the times, Tohru manages to interrupt them. Yuki envies Kyo and Kyo envies Yuki. The cat-and-mouse relationship is quite evident. In their own way they respect each other as rivals. Originally, Yuki did not hate Kyo; he actually wanted to be friends with him. But Kyo refused, as he hated Yuki simply for being the sneaky, conniving Rat.
Yuki excels in martial arts, but his respiratory system is delicate, causing bronchitis and fever if not cared properly. Hatori monitors his condition monthly.
Even if he begins as an introverted character, Yuki's glacial temper softens with the company of Tohru. He genuinely enjoys her company, she gave him the courage to begin accepting himself. Yuki even shows her his secret garden in the woods surrounding the house.