So from my understanding, the Mongols really destroyed Baghdad and burned the library housing many works from the Islamic Golden Age. What precious knowledge was lost from this destruction? Did it set humanity back hundreds of years or was the knowledge housed elsewhere too?
While more can be said, see here for /u/rakony's answer of the sack of Baghdad.
You also might find /u/XenophonTheAthenian's answer on the "destruction" of the Library of Alexandria to be illuminating.
Generally speaking, a sacking of a single library very rarely means the loss of specific scientific or technical knowledge, as there were other libraries, other centers of knowledge, and multiple copies of important texts in circulation all around the region. If a single library contained the only technical or scientific information out there, then the specific information was likely being neglected already. In the vast majority of instances, texts are "lost" because they stop being copied, not because of some dramatic single event. Time is the biggest enemy of written texts as paper degrades relatively quickly, and they are only saved due to specific conditions (e.g. Egyptian papyrus in dry desert conditions, burning of clay tablets, etc.).
Certain texts of cultural and historical importance certainly might have been lost during the sack, but in terms of technical and scientific knowledge, setting "humanity back hundreds of years" is absolutely not the case.