Algorithms lie at the very heart of computer science. An algorithm is an effective procedure, expressed as a finite list of precisely defined instructions, for solving problems that arise in applications in any domain of knowledge. All computer programs are translations of algorithms into some programming language. Often the most difficult parts of designing an algorithm are to make sure that when it is programmed in a computer, it runs as fast as possible and does what it was designed to do. This course covers the fundamentals of algorithms, focusing on designing efficient algorithms, proving their correctness, and analyzing their computational complexity. The algorithms studied are taken from a variety of applications such as sorting, robotics, artificial intelligence, searching, pattern recognition, machine learning, music, bioinformatics, arithmetic, algebra, and geometry.