Data type abstraction includes interface and implementation. interface describe what the data of the type represents, what the operations on the data are and what properties these operations may be relied on to have. implementation provides a specific representation of the data and code for the operations that make use of that data representation.
Representation-independent means the client manipulates the values of the data type only through the procedures in the interface.
We use the notation $\lceil\nu\rceil$ for “the representation of data $\nu$”.