The nucleus is a double-membrane organelle found in eukaryotic cells that contains genetic material. It has several key components: the nuclear membrane surrounds the nucleus, nucleolus forms around chromosomal regions for RNA and protein synthesis, nucleoplasm is the fluid inside the nucleus containing DNA, RNA, proteins and enzymes, and chromatin contains DNA and histone proteins that carry hereditary information. The nucleus controls cell activities and metabolic processes, stores genetic information, and synthesizes ribosomal proteins and RNA involved in protein production.