This dungeon is part of the quest line of the thieves guild. In partticular you have to walk the Pilgrim’s Path to return the Skeleton Key to Nocturnal.
there are a couple of puzzles along the way. The first is a dark room that has a few lights that shine bright circles on the ground. Simply do not walk in those circles of light and you will be fine. There are traps in the dark, usually at the top of stairs. Trigger them and take a step backwards to avoid taking dmage.
The second puzzle is when you are faced with a statue and a dead end. It took me quite a while to figure this puzzle out because the help given is “give her what she really wants” which didn’t make a whole lot of sense. All you have to do is pull the chains that you can find behind the stone heads to the left and right of the statue and the path will be open.
The last puzzle is when you find a well at the end of a tunnel. Jump down to the bottom. Simple equip some other item to continue. Sometimes the game doesn’t register it so try out a few different items if the first doesn’t work. Also try different categories of items (apparel, weapons etc) if it continues not working. The ground will dissolve and you will fall down. Return the key to finish the quest.