When you're introduced to a new puzzle concept, and the visible puzzles around that area seem to be using that idea only, is it best to finish up that area?

Right now I'm stuck on the last few puzzles of an area, so instead of banging my head against them , I kind of want to move on and come back later. Will I be screwed if I start learning other concepts and come back to the ones I'm stuck on?

You should just witness the outcome yourself.

The game is basically designed to be done in no particular order, allowing you to go somewhere else if you get stuck.

You can absolutely come back later. The whole point of the game is learning these concepts and then stacking them on top of each other to increase the complexity. I doubt you'll forget how that particular concept works. I will say though that once I figured out a concept, I solved every puzzle in that area that used it before moving on because that's just how I roll, and usually there's a curve ball or two deeper in that can change how you think about other puzzles that aren't directly related to that specific ruleset, if that makes sense. Basically I guess I'm saying that while you don't have to solve all the puzzles you know you know how to solve already, it's probably advantageous to do so even if it's starting to feel a little, "I get it already."

@davidh219: Thanks for the reinforcement! I've also never left an area until I've solved all the puzzles that use the newly introduced concept. I've accepted the notion that sometimes I have to stop playing and come back another time, and that's solved my issue every time. It just feels strange to play a game that's potentially 40+ hours for only 45 minutes sometimes, and feel the need to step away from it.

The way I've been doing it is when I find an area, I figure out as many puzzles as I can until I stuck on one. Then I walk around the area to see if I missed anything, and after that I just leave and try and find a new area. Definitely one of those games that when I come back to a puzzle sometimes it's super obvious and I solve it in seconds.

I think that most people who play games approach The Witness in the mindset of doing every puzzle in a given area in one shot, where you actually are better off getting as far along as you reasonably can before trying something else or turning the game off and coming back with fresh eyes. Banging your head against a puzzle just locks you into the wrong way of thinking and is just brutal.

There are some concepts in the game that are actually explained in multiple places. So if you're stuck on something, try doing other areas, and then when you come back your understanding of the puzzle might have increased.

You can totally come back later. Sometimes a new area might trigger something that will help you solve an earlier puzzle. Just write yourself a reminder so you don't forget that you left it undone.

I went away and back from the Monastery like four times (that last puzzle was a son-of-a-bitch), so you should totally do that.