Integrity constraints are rules that help maintain data quality and consistency in a database. The main types of integrity constraints are:
1. Domain constraints specify valid values and data types for attributes to restrict what data can be entered.
2. Entity constraints require that each row have a unique identifier and prevent null values in primary keys.
3. Referential integrity constraints maintain relationships between tables by preventing actions that would invalidate links between foreign and primary keys.
4. Cascade rules extend referential integrity by automatically propagating updates or deletes from a primary table to its related tables.