Since I did not see this talked about in the other reviews:
This is a very high grade battle anime.
The animation in the fight scenes is superb!
Only in a dedicated martial arts animation scene from a movie, or a dedicated, high budget martial arts series, are you going to see this kind of quality.
Absent are many cost saving measures of the genre, like reused animations,
or extreme closeups/motion-blur/pauses for exposition.
The framing makes it so that the moves that characters make are clearly visible, and so that the choreography can be seen clearly.
All this, as well as the excellent sound design, make the fight scenes very impactful, at
least to someone such as I,
and I have returned several times to rewatch some of the fight scenes.
The story is a pretty simple hero's journey,
which apparently infuriated some people, judging by the other reviews,
but I could find nothing wrong with it. It is Shounen after all.
It takes its time for a very profoundly executed, very emotional sub-arc in the first third of the Anime, which is not common in the genre.
The characters are very archetypal, but done in a sincere and endearing way,
and realistic enough to not be complete stereotypes.
The most stereotypical stuff is done for comedic effect, mostly.
The main character in particular is very simple, but he has clear character motivation.
Although a simple one, he has a reason to fight and to grow stronger.
Something that is sadly often missing from MCs in Shounen battle anime lately.
The title of the anime is a little misleading, because the Harem aspect of the anime is very underplayed throughout the whole season.
Compared to other Anime I would subscribe that label to, here it too is used mostly as comic relief.
I saw Danmachi compared to SAO a lot, and it certainly has a lot in common setting-wise.
If you have seen the first season of SAO, you can imagine this as being similar to the first half of the first season.
It is however not as much of a power trip as that one.
Although the MC in Danmachi has become fairly strong by the end,
he is still leagues below most of the Characters he hangs around with.
Since I enjoyed this Anime way more than I expected I would,
I would recommend anyone who likes the genre even a little to watch it.