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With the increase in our ability to manipulate biomolecular sequences, a huge amount of data has been and is being generated.Scientists from the biological sciences are the creators and ultimate users of this data. However, due to sheer size and complexity, between creation and use the help of many other disciplines is required, in particular those from the mathematical and computing sciences. This need has created a new field, which goes by the general name of computational molecular biology. In a very broad sense computational molecular biology consists of the development and use of mathematical and computer science techniques to help solve problems in molecular biology. The understanding of molecular sequences in turn requires new sophisticated techniques of pattern recognition, which are being developed by researchers in artificial intelligence. Complex tatistical issues have arisen in connection with database searches, and this has required the creation of new and specific tools. The purpose of this book is to present a representative sample of computational problems in molecular biology and some of the efficient algorithms that have been proposed to solve them. Some of these problems are well understood, and several of their algorithms have been known for many years. Other problems seem more difficult, and no satisfactory algorithmic approach has been developed so far. In these cases we have concentrated in explaining some of the mathematical models that can be used as a foundation in the development of future algorithms. This book is an introduction. This means that one of our guiding principles was to present algorithms that we considered simple, whenever possible.Computational molecular biology is expanding fast. Better algorithms are constantly being designed, and new subfields are emerging even as we write this. Chapter 1 presents fundamental concepts from molecular biology. We describe the basic structure and function of proteins and nucleic acids, the mechanisms of molecular genetics, the most important laboratory techniques for studying the genome of organisms, and an overview of existing sequence databases. Chapter 2 describes strings and graphs, two of the most important mathematical objects used in the book. A brief exposition of general concepts of algorithms and their analysis is also given, covering definitions from the theory of NP-completeness. Chapter 3 deals with sequence comparison. The basic two-sequence problem is studied and the classic dynamic programming algorithm is given. Chapter 4 covers the fragment assembly problem. This problem arises when a DNA sequence is broken into small fragments, which must then be assembled to reconstitute the original molecule. Chapter 5 covers the physical mapping problem. This can be considered as fragment assembly on a larger scale. Chapter 6 describes some of the mathematical problems related to phylogenetic tree reconstruction and the simple algorithms that have been developed for certain special cases. Chapter 7 is devoted to new field of study that has recently emerged in computational biology is genome rearrangements. Chapter 8 we describe dynamic programming algorithms for RNA structure prediction, give an overview of the difficulties of protein structure prediction, and present one important recent development in the field called protein threading, which attempts to align a a protein sequence with a known structure. Chapter 9 ends the book presenting a description of the exciting new field of DNA computing.