It is by Chris Claremont (who else), with Al Milgrom on art.
I particularly like the first cover.
It not only represents Kitty's phasing power (she can walk through walls, don't you know), but also her adventure from suburban Chicago (well, Deerfield), to Tokyo. And check out that curvature of the road/path. Clever. It continues to use the element of a vertical line in the covers throughout the series, although to less good effect after #2 or #3.
So anyway, this is but our third visit to the "Wolverine's adventures in Japan" story-well, after the miniseries and the follow-up in Uncanny from #172 (well, excluding the brief trips in #119 and #181), and the best yet. It presents a somewhat less Orientialist view of Japan than those. This is the Japan of salarymen and shinkansen.
Kitty Pryde provides our in. She's in Chicago, having left the X-Men in #183 after Colossus dumped her. For her the saying that you can't go home again is literal - her parents have divorced in the interim (Is she the first superhero with divorced parents?)
Having run away to Chicago, she then runs away to Tokyo, on the trail of Yakuza bosses who are threatening her dad, Carmen. She finds herself well out of her depth, and is handed over by Shigematsu-san, to Ogun, a demonic ninja type, who uses his mind-control powers to brainwash her. But, before she'd been captured, she'd managed a phone call to Westchester, so Wolverine is on the way.
Wolverine (or "Mr. Logan" as he is called by the person at immigration who had seen his passport) catches up with Yukio (and very definitely adds a link to the Shag Chart - on a roof, even! We probably should have added this earlier, but who is keeping score?), and outlines the problem. He makes arrangements to pick Kitty up, but instead meets an ambush by Ogun-as-Kitty herself, who he eventually recognises the smell of. After some fighting Yukio rescues Logan, Kitty and Carmen, and they recuperate at a house owned by Mariko.
Kitty is sent home to New York, but doesn't make her flight, and instead returns to Tokyo to take revenge. She's grown up now, and discards the names Ariel and Sprite and Kitten, declaring that she's a Cat now, and rather prefers the shadows anyway.
She works her way up the foodchain, and eventually confronts Ogun, who she realises will be taking all this out on Mariko, Wolverine's former fiancee (and now foster-mother of Wolverine's foster-daughter Amiko from #181). But - thankfully - she can't make that killing blow. Wolverine takes it upon himself to the deed, to protect her. He is the best at what he does, after all.
The series manages a massive maturity upgrade for Kitty - from Ariel to Shadowcat, but the real loss-of-innocence moment is not that - or the mind control by Ogun. Instead, it's the realisation that her father was no innocent victim, but an exemplar of the principle that you cannot con an honest man.
Carmen is up to his neck in it. He eventually hands himself over to the authorities at the end, mind.
Wolverine, too, grows. He has responsibilities as a father figure for Kitty - this is arguably the start of him being paired with young women (if you don't include the previous team-up with Rogue) - and more directly as a foster father for Amiko, and we see here his unwillingness to let other other people - children in particular - but also to some extent Yukio - get their hands dirty for him. We also find out more about his past - he had met Ogun, and was trained by him - on his first visit to those islands, many years ago; before he had been taken in by the Hudsons and given a home in Department H. Since Ogun was unware of it, we can conclude that something happened in between: the adamantium, the becoming an animal. The seed, in other words, of Weapon X.