This basic introduction to analysis is aimed at computer science students in their first semester. To specifically address the needs of computer science studies, the authors have based this work on the following concepts: algorithmic approach, concise presentation, software as an integral component, and emphasis on modeling and applications of analysis. The subject of the book lies at the intersection of mathematics, computer science, and applications, where algorithmic thinking plays a significant role. The chosen approach includes: the development of the fundamentals of analysis from an algorithmic perspective, the concretization of theory using MATLAB and Maple programs as well as Java applets, and the treatment of basic concepts and methods of numerical analysis. The book can be used as a foundational text for lectures starting from the first semester and as a supplementary text for a course.