This work has grown out of the lectures delivered by the author to the undergraduate and graduate students during the last fifteen years at the Bihar University, University of Wiscon- sin (1960-'61), Magadh University and to the participants (college and university teachers) of the Summer Institute of Mathematics (Patna University, 1965) in various capacities. The present volume serves as a preparation for the material to be presented in the subsequent volumes. It can be used as a text- book and can be helpful to any one who desires initiation into mathematical analysis. The presentation follows a middle course; it is neither heavy nor merely descriptive. The essential prerequisites are almost nil; the book is self-contained except at a couple of places.