I'm approaching Selune's Gaze mostly from its character concepts, rather than its mechanics, for the most part. I play some D&D 5e, but it isn't my main system, and I don't pretend to have enough system mastery to dive deep into sub-class mechanics. Still, I enjoy reading content written for all sorts of RPGs, as I find that the flavor often sparks ideas for future characters, regardless of the system. I like that this supplement focuses on a single "power source" for these five sub-classes. While I'm not too familiar with Forgotten Reamls lore or deities, I can appreciate that these sub-classes are all themed around the moon.

I love the idea of lycanthropic ancestry driving a barbarian's rage. It seems like a natural fit, in hindsight, yet I don't think I've seen it used before. Brought to an Eberron campaign, a Path of the Beast Within shifter would really double down on the theme (and now that I've reach the last page of the book, I see that this is mentioned in a sidebar—neat!). My only caution on this sub-class is granting the PC a Large size at 10th level if they have Wearboar blood. As we've seen with the recent centaur race in Unearthed Arcana, the designers have chosen to grant certain aspects of Large creatures to PCs, without going all the way. I would suggest this approach instead, granting the same carrying capacity as a Large creature and extra reach, if those are the main benefits that the sub-class seeks.

The Knight of the Blue Moon felt like an Eldritch Knight with fewer options to me. I believe sorcerers have a subset of the wizard spell list, so to grant the Knight of the Blue Moon access to sorcerer spells with the same spell progression as the Eldritch Knight and no other benefits, I'm not sure why a player would want to select this sub-class, other than flavor. Speaking of the flavor, when reading the introduction, I thought this was going to be a Paladin's oath, given the emphasis on religion. Perhaps if you really want to play a race with a bonus to Charisma, and were otherwise looking at the Eldritch Knight, this would be a good pairing for you.

The Way of the Rising Moon monk sub-class reminds me of the Jedi who are able to heal in the Star Wars Legends books. I isn't a trope I often see in RPGs, and I like it. I'm concerned about the Healing Arts class feature as written, in terms of balance. The feature allows a monk to heal a nearby ally by a number of hit points equal to the monk's Wisdom bonus. Let's say that's 3 at 3rd level. This takes place each time the monk hits with Flury of Blows. If I'm reading that right, the monk could heal up to 6 hit points by spending a single ki point (for two successful hits), and then do it two more times before each short or long rest. And that's on top of the normal damage of the Flury of Blows attacks. Granted, you can't rely on this healing, since it depends on hitting an enemy (although if you have some way of gaining advantage, that certainly helps), but it feels strong when you compare it to Healing Word, which would heal for 1d4+3 in a similar situation, but burn a much more limited resource (the cleric only has 4 1st-level spell slots per day at 3rd level). Perhaps granting temporary hit points would be a good solution here. Regardless, I still like the sub-class, and it's probably fine, as long as it doesn't step on the toes of another healer in the party.

The Moonbound Ranger archetype grants several moon- and season-themed spells. The ranger is a spell-casting warrior, casting spells that grant advantage on attacks, pushing away enemies with a sonic blast, and withering away enemies' nearby allies. Tying the four seasons to the moon is a bit of a stretch, but I like the theming.

The Lunar Magic arcane tradition offers several features that would be beneficial in a wide variety of circumstances. Proficiency in perception and darkvision are beneficial to characters who don't already have darkvision (which is the minority of 5e races). The expanded darkvision is intended to help those races that already have it, but in my experience, DMs seldom make the distinction—your mileage may vary, of course. A bonus to saving throws against magic will come in handy at 6th level. Free invisibility a number of times per day equal to your Wisdom bonus will permit a whole lot of sneaking. I don't know how this balances against other 10th-level features for wizards and other classes, as I've never played a 5e game at these levels, but it doesn't feel too far off as characters approach Tier 3. Rerolling your attack or forcing an enemy to reroll a save against your spells is helpful, but I'm not sure how it works when combined with advantage/disadvantage.

There's a small element that I would've liked to have seen different in the introduction. The first couple sections talk about religion in Waterdeep and then more specifically worship of Selune. While I knew that the book's title has Selune in it, I wasn't sure how any of this was going to tie into Dragon Heist. This explanation is given near the end of the first page. I think this should have been the very first paragraph, so the reader immediately understands how Selune ties in with Dragon Heist (because in the adventure itself, she doesn't). Once the connection is clear, the intro could go on to talk about religion and Selune's worshipers. It's fairly minor, but would've prevented me from scratching my head for the first several paragraphs.

Overall, I could easily see incorporating some of these concepts into future characters. I especially liked the Path of the Beast Within barbarian and the Way of the Rising Moon monk, and will ponder how I might incorporate them into my 13th Age games.