This book offers a concise and elegant introduction to the analysis of a real variable for mathematics students starting from their first semester. The essentials are presented clearly and with the simplest possible notation. The focus is on concepts and ideas rather than on formulas and computational skills. Beginning with the axiomatic foundation of real numbers, the central concepts of limit, completeness, and continuity are discussed. The integral and differential build upon these concepts. Each chapter includes numerous exercises, some of which develop further results. Complete solutions are provided for verification. This volume is continued in the books "A Bit More Analysis" and "Even More Analysis.".