In computer programming, inheritance describes the way in which a new class of object can be derived from one or more existing classes known as base classes. In this way it becomes possible to create new classes based upon existing classes which already provide the basic functionality required of the derived class without the need to write duplicate code to implement that functionality.

A base class is simply a class which has a virtual destructor or is itself derived from a base class but is not declared final. Classes without virtual destructors should not be used as base classes and final classes cannot be used as base classes. Derived classes inherit all the public and protected members of their base classes but none of the private members. Derived classes may override any virtual method of their base classes in order to provide a more specialised implementation of the virtual interface. Abstract base classes are a special type of base class which provide a virtual interface but need not provide a complete implementation for that interface; the derived class is expected to provide the complete implementation for that interface (if a derived class does not provide or inherit a complete interface, it too becomes an abstract base class).

There are two types of inheritance: single inheritance and multiple inheritance. With single inheritance, every class in the hierarchy derives directly from one base class such that no class appears more than once within the hierarchy. For instance, a square class may inherit directly from a rectangle class which may inherit directly from a shape class. As such we can say that a square is a type of rectangle which is a type of shape. We can therefore pass a square into any function that expects a shape or rectangle object because a square is covariant with both a rectangle and a shape. We can also say that a square is a specialisation of a rectangle, which is itself a specialisation of a shape.

With multiple inheritance, a class may inherit from two or more base classes and any base class may appear more than once in the hierarchy. For instance, boats and cars may derive from a common vehicle base class, but an amphibious vehicle is both a boat and a car and may therefore derive from the boat and car base classes. Since boats and cars both derive from the vehicle base class, this would then mean an amphibious vehicle has two vehicle base classes, one inherited from the boat class and one inherited from the car class. In many cases it would be undesirable to have two separate base classes of the same type, however through multiple inheritance we can combine these separate but common classes into a single virtual class. This is achieved by declaring the vehicle class as a virtual base of the boat and car classes. The most-derived class in the hierarchy then (indirectly) inherits just one instance of the virtual base and is then responsible for the construction of that base, rather than those classes which inherit directly from it.

Whenever we invoke a virtual method of a base class, we would rightly expect the most-derived override of that method to be invoked. This is achieved automatically through a virtual function table. While there is a runtime cost in calling virtual functions, the cost is minimal because there is no need to explicitly invoke the runtime type information on an object in order to determine which override to call. This is known as runtime polymorphism, however this only works when we refer to a base object by reference or by pointer. If we refer to a base object by value, we lose polymorphic behaviour because the object has been "sliced" to the extent that the most-derived class is now the base class itself. This behaviour is often undesirable, however modern object oriented languages, such as Java, prevent this by ensuring that all objects are passed by reference (only the reference is passed by value, not the object being referred to). In lower level languages such as C++, the programmer is entirely responsible for ensuring polymorphic objects are passed by reference rather than by value.

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