After Trigger and Instead Of Trigger

The following is from Technet:

AFTER triggers are stored procedures that occur after a data manipulation statement has occurred in the database, such as a delete statement. DDL triggers are new to SQL Server 2005, and allow you to respond to object definition level events that occur in the database engine, such as a DROP TABLE statement. INSTEAD-OF triggers are objects that will execute instead of data manipulation statements in the database engine. For example, attaching an INSTEAD-OF INSERT trigger to a table will tell the database engine to execute that trigger instead of executing the statement that would insert values into that table.

Why use an INSTEAD-OF trigger?

INSTEAD-OF triggers are very powerful objects in SQL Server. They allow the developer to divert the database engine to do something different than what the user is trying to do. An example of this would be to add an INSTEAD-OF trigger to any table in your database that rolls back transactions on tables that you do not want modified. You must be careful when using this method because the INSTEAD-OF trigger will need to be disabled before any specified modifications can occur to this table.
Perhaps a more functional reason to use an INSTEAD-OF trigger would be to add the trigger to a view. Adding an INSTEAD-OF trigger to a view essentially allows you to create updateable views. Updateable views allow you to totally abstract your database schema so you can potentially design a system in such a way that your database developers do not have to worry about the OLTP database schema and instead rely upon a standard set of views for data modifications.