Varieties of @interface declarations, some with parentheses

Question

I've noticed a variety of @interface declarations for Objective-c classes. I'd like to understand why developers declare @interface in the following ways:

// in the .h file
@interface MyClass : NSObject
// ...
@end

// in the .m file (what's the purpose of the parens?)
@interface MyClass ()
// more property declarations which seem like they can go in the .h file
@end

// again in the .m file (what's the purpose of private?)
@interface MyClass (Private)
// some method declarations
@end

Answer 1

This is just a normal class interface, inheriting from NSObject, where you declare ivars, properties and methods

// in the .h file
@interface MyClass : NSObject
// ...
@end

The following two are categories, which allow you to add methods to a class. It is not a subclass however (do not declare a method with the same name, as you won't be able to access the original one). If you have a named category of the interface (like @interface MyClass (Private)), then the implementation should be provided in @implementation MyClass (Private), in the case of unnamed categories (also called extensions), the implementation can be provided as usual. Note that extensions also allow you to add ivars to the class while (named) categories do not.

// in the .m file (what's the purpose of the parens?)
@interface MyClass ()
// more property declarations which seem like they can go in the .h file
@end

// again in the .m file (what's the purpose of private?)
@interface MyClass (Private)
// some method declarations
@end