How does Buck show love for John Thornton in The Call of the Wild?

After John Thorton saves Buck's life by rescuing him from his inexperienced, callous owners moments before they fall through the thin ice, he nurses Buck back to health, and Buck develops a lasting affection toward his new master. Buck shows his love for Thorton by biting him gently on the hand, refusing to let him out of his sight, and demonstrating his loyalty in various ways. Buck obeys every command that Thorton gives him and is even willing to jump off a cliff to prove his loyalty. When Thorton gets into a bar fight, Buck comes to his aid by viciously attacking Thorton's opponent and almost kills the man. Buck also demonstrates his love for Thorton by saving him from drowning and winning him money by pulling a thousand-pound load. After Thorton is killed by Yeehat Indians, Buck returns to the wild but once again reveals his love for Thorton by avenging his death and visiting his grave.

John Thornton is the ideal master because he not only rescues Buck from Hal and Charley's abusive ownership and nurses him back to health but also genuinely loves Buck like no master has ever loved him before. In regards to John Thornton's feelings towards Buck, London writes,

Love, genuine passionate love, was his [Buck's] for the first time. This he had never experienced at Judge Miller’s down in the sun-kissed Santa Clara Valley (London, 60).

While Buck's other masters view dogs as necessary to their business's success and a way of making a profit, John Thornton is genuinely concerned about his dogs' well-being and treats them as if they were his own children. John Thornton's adoration for Buck is evident in the way he speaks to his dog and his rough style of play. John Thornton also enjoys putting his head against Buck's head to demonstrate his affection, and he takes him wherever he goes. Under John Thornton's care, Buck begins to thrive and develops a genuine love for his master. Buck even accomplishes remarkable feats in order to make John Thornton proud and defends him at all costs. Overall, Buck has a passionate admiration and love for John Thornton because he recognizes his genuine love and appreciates his master for saving his life.

How does John Thornton's death impact Buck's future in The Call of the Wild?

The previous posts were accurate.  I would only like to echo that the death of Thornton helps to sever the bonds between Buck and humanity.  In his own mind, there had been an ongoing civil war between trust and mistrust of humans.  Buck had experienced both extremes, from loving masters to those who embodied cruelty.  One of the most rich elements of the novel is the idea that there is an insistent battle between good and evil, trust and mistrust, and that all creatures are the result of this equation.  The elements that are placed on one side of it are balanced out by another and the result is simply the consequence of what is placed on each side.  In Buck's case, the addition of Thornton's death placed more elements on the side of mistrust, which is why Buck no longer trusts humans. Yet, in the most poignant of acts, he still visits Thornton's grave to mark the presence of the last bond Buck has to humans and their world.

Thornton and his partners are surprised by a group of Yeehat Indians and murdered. Buck comes upon the bodies of his master and friends and, realizing what happened, decides to track the killers. Buck surprises them, killing a number and scattering the rest. His hatred for the Indians keeps him hot on their trail, and he eventually becomes a legend to the tribe as the dog who hunts then relentlessly. The death of Thornton frees Buck at last from human control, and he is at last able to pursue the long heard call of the wild. He joins a pack of wild wolves and presumably spends the rest of his days in the Yukon free from the control of humans.