a.rb

class Foo
  # Defining class variable on Foo
  @@bar = :alice

  def hello
    "Hello, #{@@bar}"
  end

  def bar=(x)
    @@bar = x
  end
end

foo_a = Foo.new
p foo_a.hello #=> "Hello, alice"

foo_b = Foo.new
# Foo#bar method replaces class variable @@bar.
foo_b.bar = :bob

# So, this effects to other instance of class Foo.
p foo_a.hello #=> "Hello, bob"

b.rb

class Foo
  @@bar = :alice
end

# Declare new class Bar inherits Foo
class Bar < Foo
  # You can see superclass' class variable.
  p @@bar #=> :alice

  # Try to replace in subclass
  @@bar = :john
end

class Foo
  # Above line effects to its superclass, Foo!
  p @@bar #=> :john
end

c.rb

class Foo
end

class Bar < Foo
  @@bar = :john
end

class Foo
  # Similarly, you can replace subclass' class variable from superclass.
  @@bar = :hello
end

class Bar
  p @@bar #=> :hello
end

d.rb

class Foo
  class << self
    def name
      # At here `self` is class Foo, so, instance variable will be
      # defined at class Foo.
      @name ||= :alice # default value
    end

    def name=(x)
      @name = x
    end
  end
end

p Foo.name #=> :alice
Foo.name = :bob
p Foo.name #=> :bob

p Foo.instance_variables #=> [:@name]

e.rb

class Foo
  class << self
    def name
      # At here `self` is class Foo, so, instance variable will be
      # defined at class Foo.
      @name ||= :alice # default value
    end

    def name=(x)
      @name = x
    end
  end
end

class Bar < Foo
end

Foo.name = :bob
# Because :bob will be placed in Foo class' instance variable,
# so above line doesn't effect to class Bar.
p Bar.name #=> :alice
p Foo.name #=> :bob

f.rb

class Foo
  class << self
    attr_accessor :name
  end
end

Foo.name = :alice
p Foo.name #=> :alice

g.rb

class Foo
  class << self
    attr_accessor :name
  end

  def hello
    # look up using accessor declared on Foo class
    "Hello, #{self.class.name}"
  end
end

Foo.name = :alice
p Foo.new.hello #=> "Hello, alice"

h.rb

class Foo
  class << self
    # Declare writer only
    attr_writer :name
  end

  def hello
    "Hello, #{name}"
  end

  private

  def name
    # Look up using Object#instance_variable_get.
    self.class.instance_variable_get(:@name)
  end
end

Foo.name = :alice
p Foo.new.hello #=> "Hello, alice"