There are several conflicts in the book, but the main conflict is that Buck is kidnapped and held against his will. It is resolved when he is rescued by John Thornton. When John Thornton dies, Buck eventually joins the wild.
At the judge’s home, Buck lived a life of luxury. He was very happy because he had everything he needed and was never mistreated. He was not really a working dog. He sometimes accompanied the judge’s kids hunting, but that was it. Then one day one of the judge’s employees walked him off, and he never saw home again.
Buck was mistreated by most of the people he met. These were various character vs. character conflicts. Buck vs. Manuel (his kidnapper) was one conflict. Buck vs. the man in the red sweater, who broke him, was another. Buck vs. Perrault and François, the sled team drivers, was the next. Buck’s worst conflict was with the incompetent group of sled drivers that consisted of Mercedes, Hal, and Charles. With them he met neglect and abuse. They did not know what they were doing.
In the nature of Arctic travel there was a reason why fourteen dogs should not drag one sled, and that was that one sled could not carry the food for fourteen dogs. But Charles and Hal did not know this. (Ch. 5)
This group nearly got Buck killed, and they did get themselves and the others killed. John Thornton rescued Buck. They were beating Buck for resisting. He was so exhausted he could not continue, and on some level he refused to let these people force him to pull the sled to his own death. The people really had no clue, but Buck had instincts. He was tired and hurt, but he was a strong dog. He was more valuable to John Thornton than the people.
John Thornton stood over Buck, struggling to control himself, too convulsed with rage to speak.
"If you strike that dog again, I'll kill you," he at last managed to say in a choking voice. (Ch. 5)
Ultimately, Buck does end up hearing and answering the call of the wild. He joins the wolves, but only after he loses John Thornton. He loved John Thornton, because he was the only human who ever loved him. In the wild, Buck lives by instinct.