What structure is responsible for the synthesis of proteins within a cell?

Ribosomes are the structures responsible for the synthesis of proteins within a cell. They act as the sites of translation, where messenger RNA (mRNA) is read, and amino acids are assembled into polypeptide chains, which ultimately fold into functional proteins. Ribosomes can be found floating freely in the cytoplasm or attached to the endoplasmic reticulum, specifically the rough endoplasmic reticulum, enhancing their role in protein production.

The Golgi apparatus plays a crucial role in modifying, sorting, and packaging proteins for secretion or delivery to other organelles but is not directly involved in protein synthesis. The nucleus is responsible for storing the cell's genetic material and is where transcription occurs, but it does not synthesize proteins directly. The mitochondria are primarily known for their role in energy production through ATP generation and are not involved in the actual synthesis of proteins. Thus, the primary function of ribosomes in protein synthesis distinguishes them as the correct answer.