This iteration of Batwoman carries over the plot from the Detective Comics run that's now known as Batwoman: Elegy. An excellent trade in its own right, but not necessary to read since Issue #1 of Batwoman sums up the events in a single, beautiful splash page.
The title, thus far, has been serialized with no fewer than six plot lines introduced in Issue #1, with progress being made on several of them in each subsequent issue.
Batwoman contends with the ghost “La Llorona,” The Weeping Woman, who is kidnapping and drowning children at the behest of Medusa, an organization of criminals. Department of Extranormal Operations Agent Cameron Chase has her own investment in the La Llorona case, Medusa, and an order to apprehend and unmask Batwoman.
While Kate takes comfort in her burgeoning romance with GCPD Detective Maggie Sawyer, she struggles with the rest of her home life. Once her greatest ally, Kate feels betrayed by her father over the events of Elegy and pushes him away, while at the same time trying to train her cousin, Bette, the hero formerly known as Flamebird, as a sidekick.
Batman offers her the opportunity to join Batman, Inc., but later events lead to Bette being hospitalized where she is tricked into revealing Batwoman's identity to Agent Chase. Once face-to-face with her, Bones and Chase offer Kate a chance to join the D.E.O., so she can track down the kids La Llorona kidnapped and stop Medusa, even if that puts her at odds with the rest of Batman, Inc.
Splash Pages: The art in Batwoman is gorgeous. Splash pages are liberally used to show combat and plot. For combat, these pages have a great flow to them. They manage to show the events of the fight while being a beautiful piece on their own. (See the example above.) One of my favorite scenes in the series to date is a splash page where Detective Sawyer examines a crime scene in Issue #2. Her observations are highlighted on the page and bits of the story from crime scene creep in on the edges. Admittedly, this style is a bit of a double-edged sword. The flow of information isn't always as clear as it could be, and they don't display very well in a digital format.
Well-handled Lesbian Characters: As a member of the LGBT community, I originally looked into Batwoman because it starred a lesbian character, and I couldn't be happier with how her sexuality has been portrayed. Kate being a lesbian is merely one aspect of her character; it isn't solely what defines her, and she never comes across as a stereotype. The handling of her relationship with Detective Sawyer is also well done. Sawyer is not the token girlfriend; she is a strong character and a protagonist in her own right.
Plot: There are a few weird jumps in time in Issues #2 and #3; either that, or Kate and Maggie set up two dates in the same night just a few hours apart. Also, in my opinion, it seems like Kate's decision to stop training Bette was too sudden. With how many plot threads Williams and Blackman are juggling, it's understandable and these oddities didn't occur to me until I reread the issues back-to-back and started to nitpick.
Art Oddities: As much as I love the art, some odd choices have been made, such as Kate's skin color. In her Batwoman guise, the pale skin makes her look almost vampiric, which has a nice, supernatural quality to it; however, it's not all makeup Kate applies, since she continues to be drawn in this nearly albino way when she's out of costume. This makes her stand out. It seemed pretty obvious to me that Chase would have been able to I.D. Kate as Batwoman, because no one else in Gotham is so pale.
Repairing the Kanes' Relationship: I loved the relationship between Kate and her father from Elegy. Their interactions are full of respect and love, but also have many great moments where father and daughter butt heads. While Kate has a right to be angry with her father, I really hope the two reconcile their differences, and that the Colonel goes back to being her mentor and support when she's in the field.
Flamebird's Recovery: Badly beaten by the end of Hydrology and responsible for unmasking Kate, it's going to be a while before Bette recovers, but I think repairing her body and her relationship with Kate will be fascinating to watch.
Repeal of DADT: Don't Ask, Don't Tell was one of the reasons Kate became Batwoman. Now that it has been repealed, I hope the comics will acknowledge this fact. Maybe even have Kate wrestle with the idea of rejoining the military and serving her country the way she original intended.
More Supernatural Threats: Batwoman has introduced shapeshifters (referred to as “were-beasts”) and now a ghost. I'm a sucker for modern stories involving supernatural elements, and I think making Batwoman the vigilante who tackles these threats and mysteries would be a great way to separate her from the rest of the bat-family.
Batwoman D.E.O. Agent: Now that Kate is joining the Department of Extranormal Operations, there's likely to be a lot of changes for the character. Director Bones won't make as cool a handler as the Colonel did, but, from the sounds of it, we can expect some upgrades in Batwoman's tech and having Kate go up against the rest of the bat-family on missions will undoubtedly lead to some great scenes.