Batwoman, or (less commonly) Bat-Woman, is the name of a fictional character, the female counterpart to DC Comics' popular superhero Batman. She first appeared in Detective Comics #233 (July 1956). Batwoman's real name was Kathy Kane.
Batman co-creator Bob Kane later claimed that he created Batwoman, and indeed that he drew her to resemble his wife. The fact that Kathy Kane's name matches Bob Kane's supports his claim. On the other hand, in the 1950's Kane used "ghost pencillers" such as Sheldon Moldoff and Dick Sprang to draw most Batman comics.
Batwoman was an occasional guest in Batman stories from 1956 to 1964. Batman wished for Kathy to retire from crimefighting due to the danger it placed her in -- hypocritically so, given that he expressed no such qualms over Robin's presence by his side. Nevertheless, she remained his ally.
In 1961, Batwoman was joined by her niece Bat-Girl (Betty Kane). Kathy and Betty were intended as romantic interests of Batman and Robin, respectively.
In 1964, Batwoman, as well as Bat-Girl, Ace the Bat-Hound and Bat-Mite, were dropped from the Batman titles, which were undergoing a revamp that eliminated many extraneous elements.
In the 1970's, Batwoman was revived but only appeared a few times. When Kathy eventually did retire from crimefighting, she became the owner of a circus . She was killed by the League of Assassins and the brainwashed Bronze Tiger in Detective Comics #485 (September 1979).
There was also a Batwoman on Earth 2, who was very much like her deceased Earth 1 counterpart. This Kathy Kane retired when the Batman of that world married the Catwoman. However she later came out of retirement following Batman's death when Gotham City was threatened by the return of Hugo Strange. (The question of whether there was a Bat-Girl on Earth 2 is controversial.)
Bat-Girl's career was heavily retconned after the Crisis on Infinite Earths to remove any reference to her working alongside Batman, Robin or Batwoman from her history. Batwoman has yet to be referenced in any post-Crisis comics, although the late Kathy Kane and her murder by the Bronze Tiger have been mentioned on occasion. It may be that Kathy Kane existed but was never Batwoman in the post-Crisis DC Universe.
Other Characters Named "Batwoman"
Another Batwoman appeared in the direct to video animated film Batman: Mystery of the Batwoman.
The Wild World of Batwoman was a 1966 film that was mocked in an episode of Mystery Science Theater 3000.