What exactly is the singleton class in ruby?

It seems as if I'm missing the point or misunderstanding the significance of the singleton class in Ruby. I've heard and read about it in many ways—some more complicated than others—but I'm left more confused as to what it is. Is it a class in and of itself? Is it the reason why all objects belong to "class?" The concept is fuzzy , but I believe it has something to do with why I can define a class method at all (class foo; def foo.bar ... ).

So: What is the singleton class in Ruby?

First, a little definition: a singleton method is a method that is defined only for a single object. Example:

irb(main):001:0> class Foo; def method1; puts 1; end; end
=> nil
irb(main):002:0> foo = Foo.new
=> #<Foo:0xb79fa724>
irb(main):003:0> def foo.method2; puts 2; end
=> nil
irb(main):004:0> foo.method1
1
=> nil
irb(main):005:0> foo.method2
2
=> nil
irb(main):006:0> other_foo = Foo.new
=> #<Foo:0xb79f0ef4>
irb(main):007:0> other_foo.method1
1
=> nil
irb(main):008:0> other_foo.method2
NoMethodError: undefined method `method2' for #<Foo:0xb79f0ef4>
        from (irb):8

Instance methods are methods of a class (ie defined in the class's definition). Class methods are singleton methods on the Class instance of a class -- they are not defined in the class's definition. Instead, they are defined on the singleton class of the object.

irb(main):009:0> Foo.method_defined? :method1
=> true
irb(main):010:0> Foo.method_defined? :method2
=> false

You open the singleton class of an object with the syntax class << obj . Here, we see that this singleton class is where the singleton methods are defined:

irb(main):012:0> singleton_class = ( class << foo; self; end )
=> #<Class:#<Foo:0xb79fa724>>
irb(main):013:0> singleton_class.method_defined? :method1
=> true
irb(main):014:0> singleton_class.method_defined? :method2
=> true
irb(main):015:0> other_singleton_class = ( class << other_foo; self; end )
=> #<Class:#<Foo:0xb79f0ef4>>
irb(main):016:0> other_singleton_class.method_defined? :method1
=> true
irb(main):017:0> other_singleton_class.method_defined? :method2
=> false

So an alternative means of adding singleton methods to an object would be to define them with the object's singleton class open:

irb(main):018:0> class << foo; def method3; puts 3; end; end
=> nil
irb(main):019:0> foo.method3
3
=> nil
irb(main):022:0> Foo.method_defined? :method3
=> false

In summary:

Ruby provides a way to define methods that are specific to a particular object and such methods are known as Singleton Methods. When one declares a singleton method on an object, Ruby automatically creates a class to hold just the singleton methods. The newly created class is called Singleton Class.

    foo = Array.new
    def foo.size
      "Hello World!"
    end
    foo.size  # => "Hello World!"
    foo.class # => Array
    #Create another instance of Array Class and call size method on it
    bar = Array.new
    bar.size  # => 0

    foo.singleton_methods  # => [:size]
    bar.singleton_methods  # => []