Yes. A class definition will have its own variables (state), and will have its own methods (behavior.)
The methods that a class definition has are called static methods. (Sometimes they are called class methods, but this is confusing.) A static method is a characteristic of a class, not of the objects it has created.
Important: A program can execute a static method without first creating an object! All other methods (those that are not static) must be part of an object. An object must exist before they can be executed.
Here is the example program again:
// The file StringTester.java
//
class StringTester
{
  public static void main ( String[] args )
  {
    String str1;   // str1 is a reference to an object, 
    int    len;    // len is a primitive variable of type int
    str1 = new String("Random Jottings");  // create an object of type String
                                                           
    len  = str1.length();  // invoke the object's method length()
    System.out.println("The string is " + len + " characters long");
  }
}
 
This application is similar to many you have  seen so far.
Now you can understand more details about what is going on.
Assume that a file named StringTester.java contains 
the above source code.
StringTester.main().main() is a static method, 
    it is a characteristic of the class.
    Objects of the class do not have a main() method.
    main() is a static method, 
    there will be only one main() method.
    java StringTester.
    main() method.
    main() method starts running, 
    creates a String object using new, 
    invokes its length() method, and continues.
    Remember the idea of object-oriented programming: an application consists of a collection of cooperating software objects whose methods are executed in a particular order to get something useful done. The steps listed above is how the collection of objects gets started. (In this case only one object was created.)
Say that you create a file that 
contains the definition of a class,
but the  the class contains no main() method.
Can the methods of this class ever be executed?