This volume is intended as an introduction into numerical analysis for students in mathematics, physics, and engineering. Instead of attempting to exhaustively cover all parts of numerical analysis, the goal is to guide the reader towards the basic ideas and general principles by way of considering main and important numerical methods. Given the rapid development of numerical algorithms, a reasonable introduction to numerical analysis has to confine itself to presenting a solid foundation by restricting the presentation to the basic principles and procedures. The book includes the necessary basic functional analytic tools for the solid mathematical foundation of numerical analysis. These are indispensable for any deeper study and understanding of numerical methods, in particular, for differential equations and integral equations. Particular emphasis will be given to the question of stability--especially to well-posedness and ill-posedness. The text is presented in a concise and easily understandable fashion and can be successfully mastered in a one-year course.