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The complexity barrier of solvable computational problems is nowadays pushed at equal rates by the rapid development of both computers and algorithms, hardware and software. This textbook on Numerical Analysis is a first introduction to the fundamentals of efficient algorithms. The selection of topics and the presentation of the material has been made with a strict view to the needs of Computational Science. Important concepts of modern numerical analysis are illustrated with the simplest type of problem to which they are applicable. The main aim of the book is the development of algorithmic thinking and intuition.