Chapter 1-2: George and Lennie establish what their dream is.
Chapter 3-4: Candy's dog is put down.
Chapter 5: Lennie breaks Curly's Wife's Neck
George and Lennie want their dream to come true. They want to have a farm of their very own. Lennie wants rabbits on their farm. This is a theme of hopes and dreams.
Candy had his dog put down by Carlton. The dog was shot in the back of the head. This was the same place Lennie was shot, with the same gun. This is a theme of foreshadowing.
Chapter 6: George kills Lennie
Lennie has been unintentionally killing things. First, was a mouse. Then, a puppy. And now, Curley's wife. His love for soft things has gotten the things he has touched killed. This is a theme of repetition.
George now has to kill Lennie. This is because Lennie has done a bad thing, killing a human being. This is for his own good. This is a theme of death.