This book is a straightforward and comprehensive presentation of the concepts and methodology of elementary real analysis. Targeted to undergraduate students of mathematics and engineering, it serves as the foundation for mathematical reasoning and proofs. The topics discussed are logic, methods of proof, functions, real number properties, sequences and series, limits and continuity and differentiation and integration (Riemann integral and Lebesgue integral). The book explains the concepts and theorems through geometrical and pictorial representation. Limits of sequences and functions, topology of metric spaces, continuity of functions and the Cauchy sequence have been thoroughly discussed in the book.