Codd's Rule outlines 12 rules for relational database management systems (RDBMS) including: storing data in tables with rows and columns, guaranteeing access via table name, primary key and attribute, treating NULL values systematically, using a powerful yet well-structured query language, and ensuring logical and physical data independence. Key concepts in relational databases include tuples (rows), attributes (columns), attribute domains defining value types, relation schemas describing table structures, and relational integrity constraints like key, domain and referential constraints. The relational database design process involves defining the purpose, gathering and organizing data in tables with primary keys, creating relationships between tables, and refining the design through normalization.