Database normalization is a systematic approach to organizing data within a relational database. It involves several stages, specifically 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) represents the foundational level of normalization. This form mandates that the data within a relational database is devoid of repeating groups. In practical terms, this means that each column must contain atomic values, ensuring that no single column can hold multiple values that would lead to ambiguity in row retrieval. Furthermore, every table should be structured so that it can be uniquely identified by a primary key.

Second Normal Form (2NF) enhances the principles established in 1NF by ensuring that all non-key attributes are fully functionally dependent on the primary key. This condition prevents any partial dependency on the primary key attributes. For instance, in a table with a composite primary key, each non-key attribute must rely on the entire set of primary key columns rather than just a subset.

Third Normal Form (3NF) takes normalization a step further by stipulating that all non-key attributes must not have dependencies on other non-key attributes. In simpler terms, it prohibits transitive dependencies within the table. This means that if one column depends on another non-key column, which in turn depends on the primary key, such a relationship is not permissible in 3NF.

Boyce-Codd Normal Form (BCNF) is a more stringent version of 3NF. It requires that for every non-trivial functional dependency $X \rightarrow Y$, the set $X$ must qualify as a superkey. In other words, if a column is dependent on another column, that other column must be a unique key within the table.

Fourth Normal Form (4NF) addresses the issue of multi-valued dependencies. It asserts that for any non-trivial multi-valued dependency $X \rightarrow\rightarrow Y$, the set $X$ must be a superkey. This means that no combination of attributes should create multiple independent multi-valued facts about a single entity.

Fifth Normal Form (5NF), also known as Project-Join Normal Form (PJNF), concerns scenarios where data can be reconstructed from smaller pieces of information, allowing for reduced redundancy. It requires that every join dependency within the table must be implied by the candidate keys.

By adhering to these normalization forms, databases can achieve greater integrity and reduced redundancy, ultimately leading to more efficient data management.