As I did with "The Greatest Joker Stories Ever Told" discussion, I borrowed the title from a tpb collection but I plan to go beyond the actual contents of the collection itself. Catwoman has the unique distinction of appearing in the first three consecutive issues of Batman.
BATMAN #1 - "The Cat" - Kids who bought Batman #1 certainly got their money's worth, and you can take it from me because I was one (if you count the Famous 1st Edition TE, which I do). Not only did it contain the first appearance of Hugo Strange and the first two appearances of the Joker, but it also had the first appearance of the Catwoman, known then as simply "The Cat." Mrs. Martha Travers is hosting a high society get-together on her yacht, the Dolphin, and she will be wearing her emerald necklace worth a half million dollars. Batman is busy on another case, but he uses his contacts as Bruce Wayne to get Dick Grayson a job as steward. Sure enough, the necklcae is stolen almost immediately. The suspects are...
- Denny - Mrs. Travers' nephew
- Miss Pegg - Denny's elderly guest who has a sprained ankle
- Roger - Mrs. Travers' brother
- Dr. Wallace - Mrs. Travers' doctor
All of these people (except Miss Pegg) have motive. Just prior to the theft being discovered, Dick recovers a note from "The Cat" implicating Denny. Just after the theft, the "Coast Guard" arrives, but it is really just another gang of thieves after the necklace. They are disappointed to learn the emerald necklace has already been stolen, but content themselves with robbing the rest of the guests and speeding away in their launch. But Dick had changed to Robin and sneaked aboard beforehand. By this time, the trail had gone cold an Batman's other case and he catches up with the criminals. He and Robin subdue them, and return to the Dolphin with the stolen loot.
They arrive in the midst of a costume party, and Batman wins the prize trophy cup. He dumps the recovered jewelry into it and reveals that he is the real Batman. then Robin sets off the ship's fire alarm, and Batman observes that "Miss Pegg" is running pretty fast for an elderly woman with a sprained ankle. He also notices her shapely legs. After he and Robin catch her, Batman removes her wig and make-up revealing a beautiful young woman: The Cat! She is wearing the emerald necklace beneath the badage wrapping her supposedly "sprained" ankle. then Denny arrives, pulls a gun on Batman, and is quickly knocked unconscious by a left uppercut. Batman and Robin personally take the Cat into custody, but Batman allows her to escape from the boat on their way back to the harbor.
"Lovely girl!" he muses. "What eyes! Say... mustn't forget I've got a girl named Julie. Oh, well... she still had lovely eyes! Maybe I'll bump into her again sometime..."
"Hmmm..." observes Robin.
BATMAN #2 - "Joker Meets Cat-Woman" - An item in the Gotham Herald reveals: "E.S. Arthur to Ship Priceless Pharaoh Gems to British Museum - Collection Valued at $10.000.00." Knowing that the Joker will be her primary competitor, the Cat, disguised as an old woman pedling gum, stakes out the hospital in which the he is recovering after accidentally stabbing himself in issue #1. Crime Syndicate, Inc. breaks the Joker out of the hospital and, as the Cat doffs her disguise, Batman scoops her up in his arms and whisks her into the Batmobile. Fearing that Batman will turn her in to the police, she offers to reveal all she knows about the Joker in return for her freedom. Batman agrees, and she tells him that the Crime Syndicate has taken Joker to Weasel's hunting lodge. Batman lets her go, but sends Robin to track the "radioactive substance" her shows picked up from the floor of the car.
Batman get to Weasel's hunting lodge just in time to witness the Joker betraying his men. Batman captures the other criminals, bit the Joker gets away. Meanwhile, Robin has followed the Cat to E.S. Arthur's castle. she had previously "won his affections," but she arrives to find him already dead, poisoned earlier by the Joker. As she is stealing the jewels, the Joker arrives. As he holds her at gunpoint, Robin swings through the window and disarms him. after a brief fight, the Joker knocks Robin unconscious. As the Joker is about to inject him with lethal Joker venom, the Cat offers him the jewels in exchange for the boy's life. Suddenly, Batman arrives, swinging an a chandelier. He and the Joker start to dual with two swords hanging on disply above the fireplace.
The Joker drives the him off the balcony, but Batman manages to save himself. By the time he climbs back to the balustrade, the Cat and the wounded Robin have barricaded themselves in the library, and the Joker has set it afire with burning arrows fired from a crossbow. The Batman knocks the Joker out and leaves him behind as he rescues the Cat and Robin using a rope ladder from the Batplane. As soon as they are clear of the fire, however, the Cat leaps into the water below with the jewel cask, but the Batman managed to slip the jewels out while they were still climbing the ladder. Is this "The end of the Cat-Woman?" Bill finger wants to know. Apparently not, because she's back again in...
BATMAN #3 - "The Batman vs. the Cat-Woman!" - In the story, the Cat (also referred to as the "Cat-Woman") wears an orage dress, red cape, and life-like cat-head mask. As the story opens, she is looting a penthouse. The public is up in arms, and Police Commissioner Gordon appoints McGonigle of the plainclothes squad to bring her in. When Bruce Wayne gest word of the manhunt, he too sets out after her, but pointedly leaves Robin behind. He soon comes upon three men attacking another in an alleyway. Two of the men flee, but he brings down the third. The victim is D. Calvert, secretary of the Diamond Syndicate. He is mortally wounded, but manages to relay a cryptic warning about an upcoming diamond shipment before he expires. He doesn't have any diamonds on him, so robbery wasn't the motive. While Batman is seeing to the dying man, his attacker recovers, knocks Batman out from behind, and is picked up by his tweo confederates.
When Batman awakens, he is wearing handcuffs, placed there by McGonigle. Batman knocks the detective unconscious, then frees himself. when McGonigle awakens, he decides not to mention anything about the Batman in his report. Bruce Wayne visits police headquarters just as Commissioner Gordon is about to leave to interview the managers of the Diamond Syndicate, Darrel, Blake and Hoffer. They are planning a show in which the diamonds are to be displyed by professional models. the night of the show, the first model wears a ruby necklace. the second models a diamond clip. the third is wearing an arry valued at close to a million dollars. Suddenly, the "model" reaches into her handbag and hurls a flashbomb at the stage.
In the confusion, she darts into the elevator. On the way down, she takes off her blonde wig reavealing herself to be the Cat(-Woman) in disguise. Then she puts on her cat-head mask (because there's noting less suspicious than a woman in an evening dress wearing a cat-mask). As soon as she is outside, however, she is forced into a car by four men who were expecting her. Then, out from behind, darts a miniature racer driven by Robin. Robin trails them and notifies Batman by wireless where they have gone. On his way there, Bayman stops off an Darrel's penthouse and forcibly takes him along. When they arrive, Darrel is surprised to see Hoffer holding a gun on the Cat.
"You rat!" accuses Darrel. "When you and I decided to hire the Cat to steal the diamonds because we needed money, I didn't expect you to double-cross me!"
"I suddenly decided you and the Cat would be taking too much of a cut!" confesses Hoffer. "I'm going to get rid of both of you!"
Before he has a chance to, though, Batman and Robin burst in and capture the whole kit and kaboodle of them. Unfortunatley he has to turn in the Cat as well, but she understand, and thanks him for saving her life by kissing him on the lips. Batman is so nonplussed that she is able to shove him away and dart out the door. She takes off in the gangsters car, but Batman stops Robin from following in his mini-racer, explaining that "she's too far away for you to catch up!" Later, Batman drops all of the stolen jewelry and the evidence in from of McGonigle, but it still doesn't win him over to Batman's side. Meanwhile, the Cat muses, "I sort of wish the Batman were driving this car -- and I were sitting beside him... and we were just another boy and girl out for a ride on a moonlight night. that would be sort of... of... nice!!"

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It will take me a while to find the exact source, but at some point during all the "Countdown", "52" and "Final Crisis" issues it was revealed that Duela Dent is the daughter of the Jokester - the heroic counterpart of the Joker in Earth-3.
I think it was revealed in "Countdown Presents: The Search for Ray Palmer: Crime Society (2007) #1".
You need look no further. Actually, there is quite a bit about Duela Dent online, in Wikipedia and elsewhere. Me, I'm a big proponent of the K.I.S.S. school of thought ("Keep It Simple, Stupid"). According to Wikipedia: "Duela's last Pre-Crisis appearance is in Tales of The Teen Titans #50, as a guest at Donna Troy's wedding where she appears to be a middle-aged matron. Dick Grayson notes that he had finally realized that she was too old to be Two-Face's daughter; she agrees, then disappears before he can take the matter further." I'm okay with that. Some of the later revisions are now regarded as "a time glitch caused by Zero Hour." I'm okay with that, too. The half-remembered story I was thinking of is from Titans Secret Files #1 in which she appeared "insisting to anyone who would listen that the Titans would soon contact her about membership." In that story she also claims that she is the daughter of Doomsday.
Batman writer Len Wein reintroduced Selina Kyle as a sub-plot/suporting character in #310. First, she calls Bruce Wayne out of the blue to discuss her planned investments in Wayne Enterprises and they end up having lunch. Next, they have dinner in #313. In #314, Selina learns that Bruce Wayne had her investigated by Lucius Fox, and in #315 she confronts him about it. Bruce reconciles with Selina in #317. In #318, they go to a flying disco aboard a 747. When the chartered plane lands, their arrival at the gate is delayed by the unloading of recently-discovered "cat-god artifacts" enroute to Riverside Museum. The next night (#319), Bruce Wayne hosts a costume party at Wayne Manor. He is dressed as Henry the VIII, Selina Kyle as Catherine of Aragon. Bruce is soon called away by an urgent summons from Alfred. Later, he returns, just as his guests are about to be robbed by the Gentlman Ghost (three of them, actually). Batman appears and deals with them. In #321, Selina Kyle is one of several people abducted by the Joker, but Batman frees them.
In #322, Selina Kyle peruses a scrapbook of her exploits as Catwoman. The next days she visits her doctor, who confirms that she has a rare exotic disease and gives her six months to live. He further reveals that the ancient Egyptions had a cure, but it has been lost to the ages. Later she visits the Riverside Museum and learns that the exhibit on display includes Egyptian herds in hermetically sealed urns. She gets into an argument with the guesr when she tries to touch one of the urns. That night she tries call call Bruce Wayne but he is unavailable. She contemplates "helping herself" as she eyes her costume hanging in the closet. Later still, the guard at the Riverside museum sees a cat-garbed figure making off with the Egyption urns who scratches him with a clawed glove. All this sets the stage for "The Return of the Catwoman" in...
BATMAN #323 - "The Shadow of the Cat!"
When Batman learns of the robbery, he swings off to confront Selina Kyle about it in her hotel romm, but she demies all knowledge of the event. She evades capture by distracting him with her cat and swinging off using Batman's own rope. the next day Catwoman appears at wayne Foundation seeking assistance from Bruce Wayne, but he insists that she turn herself in, first. Knowing she won't live long enough to stand trial and clear her name, she runs. Using their own respective methods, Catwoman and Batman both follow clues individually to a secret tunnel beneath hte Apex Import & Export Building used by bootleggers back during Prohibition. The both soon fall into a...
Deathtrap: ...a sticky "cat's cradle" system of cables covered with a polymer adhesive set by the story's true thief... Catman. The cat's cradle stretches and contracts in such a way as to tear anyone caught in it apart.
Is This the End of the Catwoman...?
BATMAN #324 - "The Cat Who Would be King!"
In true villain fashion, Catman leaves them alone giving Batman the opportunity to devise an escape. Catman leave a piece of his boot behind, and in another well-worn cliché, Batman determines that he headed to Greece by the dirt on the heel. Catman's plan is to trade the Egyptian artifacts to a collector in exchange for an island, which he plans to turn into a super-villain sancuary (another cliché). The collector, Andros Akropolis, double-crosses Catman just as Batman and Catwoman arrive, giving Catman the chance to escape with the loot. As he runs, Akropolis shoots and hit him, but he is saved, supposedly, by the "mystic cloth" his costume is made from. Selina is suffering the last-stage effects of her illness.
Akropolis and his men are on the private island he owns and technically have committed no crime. They leave, waring Batman not to be there when he will return with "a small army." Catman reappears and attacks Batman from behind. Then he grabs Catwoman, but she breaks free. In the scuffle that follows, Catman falls into an active geyser Catwoman tries to save him, but his cape rips off in her hands and he is killed, taking the cure with him. By the time they get back to the States, Catwoman's disease has gone into remission, for no particular reason whatsoever. Or was it because of the remains of Catman's "mystic" cloak? Selina Kyle breaks up with Bruce Wayne in #326 and leaves gotham, and Len Wein leaves Batman with #327.
BATMAN #332-335:
Batman #332 begins the four-part "Lazarus Affair," but we are more concerned here with the back-up feature in #332-333, which crosses over into the main story in #334. Actually, the Catwoman back-ups are not true "solo stories" in that they don't stand alone. they are merely the sub-plot concerning Catwoman grouped together. In part one of the main story, Robin asks Catwoman for help, but it's not really possible to follow Catwoman's "story" on its own, divordec from the main plot. In any case, the plots are folded together in #334, but as soon as Talia comes into the plot, Catwoman fades into the background. Then in #335, Catwoman, Robin and King Faraday literally walk out of the story ten pages from the end.
MEANWHILE ON EARTH-2:
In Superman Family #211, Bruce Wayne marries Selina Kyle. According to my sources, "Two Face" also appears in this issue, although I suspect Harvey Dent of Earth-2 is one of the guests at the wedding, but I don't have this issue so I'll leave it up to someone else (probably Philip) to confirm or refute.
Yes, Harvey KENT is one of the guests and jokes with Clark about possibly being related!
If Roy Thomas had written it, they would be.
E. Nelson Bridwell wrote it and you can be darn-sure that he knew the Kent family tree, even on Earth-Two!
There's a previous Catwoman appearance in The Batman Family #17 (My'78) where the Huntress travels to Earth-One to consult Batman about her career because she can't tell her father, the E-2 Batman.
Our Caped Crusader passes the buck to Batwoman (though later it would be revealed that there is an E-2 Batwoman) who brings her to Batgirl.
Meanwhile Madame Zodiac recruits Catwoman and Poison Ivy to commit a crime that leads to a confrontation with the three Bat-Ladies, forcing the Huntress to battle a still-criminal version of her late mother!
BATMAN #345-346 - "Terror Train" and "In the Land of the Dead"
"In the early 1980s, Selina Kyle returned, swearing she had reformed and, with Bruce Wayne's help, became a legitimate businesswoman. She even began romancing Wayne while occasionally fighting side by side with The Batman. this led to some very memorable subplots from writers Len Wein and Marv Wolfman, but they did not lead to very strong Catwoman-oriented stories for this collection. This interpretation did lead to a short-lived series of backup features starring the adventurous Catwoman. The first two installments are presented here, representing the best of that run." -- Robert GreenBerger, The Greatest Batman Stories Ever Told Vol. 2.
In part one, Catwoman must solve the mystery of passenger train cars that seem to disappear and reappear between Gotham and Chicago. In part two she discovers that the detective who hired her is an ex-Nazi looking for a hydrogen bomb formula hidden on the train. At this point I am not going to try to list every Catwoman appearance, only the "strong Catwoman-oriented stories."
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