This book is an attempt to present the concepts of Limit of Functions, Theory of Equations including Cubic and Bi Quadric Equations, Trigonometry and Real analysis which includes Sequences of Real Numbers, Infinite Series, Indeterminate Form and Expansions of Functions under CBCS pattern to the students of Under Graduate Classes. Earnest efforts have been made to present the subject matter in a simple manner. The solved problems are given in details so that the learners can easily understand the subject matter. Theorems and problems have been stated and proved carefully. My aim is to draw the attention of the students to study the book thoroughly so that they can understand without any other help.