Solid Hardwood, Engineered and Laminate Flooring - How to repair parquet that has got wet?

There are a few places where a bunch of the pieces of parquet flooring has lifted, prolly due to getting wet. How do you go about getting these pieces glued back down? Also, would I have to do anything the floor to prep it to be re-glued? We rent and the complex owners are supposed to fix it for us, but they have been dragging their asses and we are fed up waiting.

I read one post on here about using Liquid Nail, would that do the trick for my scenario? Afterwards, would I need to place a board with a weight on it?

Ya, the liquid nails will work. Get a small jug of mineral spirits, while your getting the liquid nails, for glue ooze clean up.