This text provides the fundamental concepts and techniques of real analysis for students in all areas, helping one develop the ability to think deductively, analyze mathematical situations, and extend ideas to a new context. The fourth edition maintains the same spirit and user-friendly approach as its predecessors with additional examples and expansion on logical operations and set theory. Key content revision includes introducing point-set topology before discussing continuity, providing a more thorough discussion of limsup and liminf, covering series directly following sequences, adding coverage of the Lebesgue integral and the construction of the reals, and drawing student attention to possible applications wherever possible.