This textbook features a clear and modern structure and is designed for a comprehensive foundational education. It is the first volume of a two-part introduction to analysis, aimed at students of mathematics and related fields (such as physics, computer science, and engineering) as well as their instructors. Central fundamental concepts are introduced and discussed early on—initially not in a general sense, but within an appropriate and manageable framework. These concepts are then explored in greater depth with increasing complexity and examined from various perspectives. A wide range of examples and exercises illustrates the interconnections and integration of analysis with other areas of mathematics, providing students with extensive opportunities to deepen their knowledge and understanding of the subject.