Explain the different normal forms in database normalization.

Database normalization includes First Normal Form (1NF), Second Normal Form (2NF), Third Normal Form (3NF), Boyce-Codd Normal Form (BCNF), Fourth Normal Form (4NF), and Fifth Normal Form (5NF).

First Normal Form (1NF) is the most basic level of normalization. It requires that the data in a relational database is free of repeating groups. In other words, each set of column must have a unique value, such that multiple columns cannot be used to fetch the same row. Additionally, each table should be organised in such a way that it can be identified by a unique key.

Second Normal Form (2NF) builds on the rules of 1NF by ensuring that all non-key attributes are fully functional and dependent on the primary key. This means that there should be no partial dependency of any column on the primary key. For example, if a table has a composite primary key, then each non-key attribute should be dependent on the full set of primary key columns and not on just a part of it.

Third Normal Form (3NF) goes a step further by ensuring that all non-key attributes are not dependent on other non-key attributes. This means that there should be no transitive dependency within the table. In simpler terms, if a column is dependent on another column, which is in turn dependent on the primary key, then this is not allowed in 3NF.

Boyce-Codd Normal Form (BCNF) is a stronger version of 3NF. It requires that for every non-trivial functional dependency X -> Y, X should be a superkey. This means that if a column is dependent on another column, then the latter column should be a unique key in the table.

Fourth Normal Form (4NF) deals with multi-valued dependencies. It requires that for any non-trivial multi-valued dependency X ->> Y, X should be a superkey. This means that there should be no set of attributes that can lead to more than one independent multi-valued facts about an entity.

Fifth Normal Form (5NF), also known as Project-Join Normal Form (PJNF), deals with cases where information can be reconstructed from smaller pieces of information that can be maintained with less redundancy. It requires that every join dependency in the table is implied by the candidate keys.