Sasuke's ambitions were first asked about early on in the series. He simply states he wants to "resurrect his clan", and "to kill a certain someone". At the time, we knew nothing about his motivations, but I'll do my best to discuss it here.
Sasuke's first ambition mentioned is to kill someone, who is his elder brother, Itachi. Itachi, who will be discussed later, is Sasuke's older brother. To achieve this ambition, as he calls it, is more important than anything else; It's his top priority. Eventually, we learn that he'll stop at nothing to kill him. To learn more about his brother and his responsibility for the massacre, go here.
His other (somehow less important) ambition is to resurrect his clan. The context of the words aren't very clear. Some people assume he wants to start the clan over from scratch, beginning with him. However, Sasuke doesn't look like he's interested in starting a family. Others think of this as bringing his clan back from the dead. This one slightly makes more sense since Orochimaru does have the ability to bring people back from the dead. Sasuke left Konoha to join Orochimaru, if you didn't already know. I'm not going to get into this too far, since it'll eventually be revealed.
Andddd… Sasuke actually had dreams once *gasp*. One of them was to surpass Itachi as a ninja. Sasuke worked hard live up to the clan's and his father's expectations, but he wanted to become better than his brother as well. He also has another one. This is revealed later, far into the series, around chapter 220. After learning about one of the major roles the Uchihas play in the community, Sasuke says he wants to become involved with it when he grows up. He wanted to become a part of the police force that the Uchiha clan runs in Konoha. This one is actually more attainable and realistic than any of his other ambitions, dreams, and whatnot. This dream shows an example of how he used to be before the incident, when he wasn‘t nearly as cynical; he too was once an ordinary, normal kid who had a dream.
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