"In recent years, object-oriented programming has emerged as the dominant computer programming style, and object-oriented languages such as C++ and Java enjoy wide use in academia and industry. This text explores the formal underpinnings of object-oriented languages to help the reader understand the fundamental concepts of these languages and the design decisions behind them.
The text begins by analyzing existing object-oriented languages, paying special attention to their type systems and impediments to expressiveness. It then examines two key features: subtypes and subclasses. After a brief introduction to the lambda calculus, it presents a prototypical object-oriented language, SOOL, with a simple type system similar to those of class-based object-oriented languages in common use. The text offers proof that the type system is sound by showing that the semantics preserves typing information. It concludes with a discussion of desirable features, such as parametric polymorphism and a MyType construct, that are not yet included in most statically typed object-oriented languages."

Objects:

An object literally means a  'material thing'  that is capable of being presented ot the senses For our purpose, and object is a tangible entity that may exhibit some well-defined behavior, For example, let us consider a tennis ball:

#  A tennis ball is a tangible entity, with a visible boundary.
#  A tennis ball has a specific defined purpose ( such as bouncing).
#  You can direct a specific action towards a tennis ball by hitting it with a racquet or by tossing it.

But the definition of an object is not limited to merely something that can be seen, held and touched, such as a tennis ball or a car, For the purpose of software development, the definition of an object needs refinement, For example, consider the Acme Nut and Bolt Company. And organization does not have a visible boundary, unlike a tennis ball. While it does not possess a physical boundary, it does have a conecptual boundary. Like all organization, it has a specific defined purpose, and one can direct a specific action towards it, Thus, the Acme Nut and Bolt Company is an object.