Synopsis The present publication is divided into two sections i.e., Real Analysis and Complex analysis. Section on Real Analysis covers Sequences of Real Numbers; Sequences of Rational Numbers; and Limits and Continuity, while the section on Complex Analysis covers Analytic Functions and Power Series; Conformal Mappings and Complex Integration and Calculus of residues. The topics included in the text are according to the new pattern of University Grants Commission and is useful to the students of several Indian Universities. The method of presentation is very clear and lucid which can be easily followed by the students.