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These are my lecture notes from CS681: Design and Analysis of Algo rithms, a one-semester graduate course I taught at Cornell for three consec utive fall semesters from '88 to '90. The course serves a dual purpose: to cover core material in algorithms for graduate students in computer science preparing for their PhD qualifying exams, and to introduce theory students to some advanced topics in the design and analysis of algorithms. The material is thus a mixture of core and advanced topics. At first I meant these notes to supplement and not supplant a textbook, but over the three years they gradually took on a life of their own. In addition to the notes, I depended heavily on the texts A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Algorithms. Addison-Wesley, 1975. M. R. Garey and D. S. Johnson, Computers and Intractibility: A Guide to the Theory of NP-Completeness. w. H. Freeman, 1979. R. E. Tarjan, Data Structures and Network Algorithms. SIAM Regional Conference Series in Applied Mathematics 44, 1983. and still recommend them as excellent references.