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This book is based on the Computational Molecular Biology course at the Computer Science Department at Pennsylvania State University (1992-1995) and then at the Mathematics Department at the University of Southern California (1996-1999). It is directed toward computer science and mathematics graduate and upper-level undergraduate students. Parts of the book will also be of interest to molecular biologists interested in bioinformatics. The rationale of the book is to present algorithmic ideas in computational biology and to show how they are connected to molecular biology and to biotechnology. To achieve this goal, the book has a substantial "computational biology without formulas" component that presents biological motivation and computational ideas in a simple way. This simplified presentation of biology and computing aims to make the book accessible to computer scientists entering this new area and to biologists who do not have sufficient background for more involved computational techniques. The book concentrates on computational ideas rather than details of the algorithms and makes special efforts to present these ideas in a simple way. Of course, the only way to achieve this goal is to hide some computational and biological details and to be blamed later for "vulgarization" of computational biology. Another feature of the book is that the last section in each chapter briefly describes the important recent developments that are outside the body of the chapter. The book covers both new and rather old areas of computational biology. For example, the material in the chapter entitled Computational Proteomics, and most of material in Genome Rearrangements, Sequence Comparison and DNA Arrays have never been published in a book before. At the same time the topics such as those in Restriction Mapping are rather old-fashioned and describe experimental approaches that are rarely used these days. The reason for including these rather old computational ideas is twofold. First, it shows newcomers the history of ideas in the area and warns them that the hot areas in computational biology come and go very fast. Second, these computational ideas often have second lives in different application domains.