The Joker was a straightforward homicidal maniac killing more than 3 dozen people in his first run in the Batman series. In his first appearance, he left his victims with smiles on their faces after their deaths, something that has become a trademark for the character throughout his many years in publication. In his first appearance, the Joker challenged both the police department as well as Batman when he threatened to kill three people.
The Joker trapped Robin, d**k Grayson, and was prepared to kill him until the Batman showed up and stopped him. This story would be retold in 2005's Batman: The Man Who Laughs.
In "The Joker Walks His Last Mile" Joker is sentenced to the electric chair. He escaped by faking his own death and when captured later on he could not be electrocuted due to the Double Jeopardy law. The Joker pretended to be a good citizen but soon fell into his old habits.
In his last appearance in Earth-Two Continuity, Bruce Wayne was revealed to be The Batman, and recently died. The Joker refused to believe this and began to destroy Gotham City hoping that Batman simply retired. d**k Grayson impersonated the Batman long enough for Joker to be taken into custody.
Due to the Comics Code Authority Censorship Board in the 50's and 60's, DC was forced to make the Joker a seemingly harmless nuisance. In 1964, with a new editor heading the series the Joker was hardly ever seen. The main thing to take away from the Silver Age Joker is his appearance as Red Hood before becoming the Joker. There has never been a distinct break in where the Golden Age Joker ended and the Silver Age Joker began.
There would be profound revisions of the Joker in the early 70's by Dennis O'Neil and Neal Adams. In Batman #251 the Joker returned to his homicidal roots and enjoyed matching wits with the Batman.