The nucleus is a spherical organelle found in eukaryotic cells that controls cell functions and contains DNA. It is surrounded by a double membrane and contains chromatin, nucleoplasm, and one or more nucleoli. The nucleus controls gene expression and protein synthesis, regulates cell growth and division, and maintains hereditary material. It allows for the exchange of molecules with the cytoplasm through nuclear pores in its membrane. The nucleus contains the cell's genetic material and plays a key role in controlling cell activities and functions.