Object$-$Oriented Software Design $($OOSD$)$ constitutes one of the most important and most popularly used software design frameworks, and is routinely applied to software design projects covering all fields, both small$-$ and large$-$scale. As a Computer Systems Engineering student, understanding this approach of software design is a core competency that you are expected to have.

Discuss in detail the following aspects of the object$-$oriented software design framework:

$1.$ The OOSD concepts of abstraction$,$ encapsulation, inheritance and polymorphism

$2.$ Use of the Unified Modeling Language $($UML$)$ in OOSD

$3.$ The key stages of OOSD, from requirements analysis through to implementation and testing

$4.$ The role of the following UML diagrams in OOSD:

Use case diagram

Class diagram

State diagram

Activity diagram

Communication diagram

Sequence diagram

Include pictorial illustrations of all the concepts, accompanied by detailed explanations in your documentation.