Progress in the study of data structures and algorithm design has continued. Out of this recent work has come many good ideas which we believe should be presented to students of computer science. It is our purpose in writing this book to emphasize those trends which we see as especially valuable and long lasting. The most important of these new concepts is the need to distinguish between the specification of a data structure and its realization within an available programming language. This distinction has been mostly blurred in previous books where the primary emphasis has either been on a programming language or on representational techniques. Our attempt here has been to separate out the specification of the data structure from its realization and to show how both of these processes can be successfully accomplished. The specification stage requires one to concentrate on describing the functioning of the data structure without concern for its implementation. This can be done using English and mathematical notation, but here we introduce a programming notation called axioms. The resulting implementation independent specifications valuable in two ways: (1) to help prove that a program which uses this data structure is correct and (2) to prove that a particular implementation of the data structure is correct. To describe a data structure in a representation independent way one needs a syntax. This can be seen at the end of section 1.1 where we also precisely define the notions of data object and data structure. This book also seeks to teach the art of analyzing algorithms but not at the cost of undue mathematical sophistication. The value of an implementation ultimately relies on its resource utilization: time and space. This implies that the student needs to be capable of analyzing these factors. A great many analyses have appeared in the literature, yet from our perspective most students don't attempt to rigorously analyze their programs. The data structures course comes at an opportune time in their training to advance and promote these ideas. For every algorithm that is given here we supply a simple, yet rigorous worst case analysis of its behavior. In some cases the average computing time is also derived. The growth of data base systems has put a new requirement on data structures courses, namely to cover the organization of large files. Also, many instructors like to treat sorting and searching because of the richness of its examples of data structures and its practical application. The choice of our later chapters reflects this growing interest.