This section introduces the branch of mathematics called calculus, derivative, limits and algebra of limits. The derivative is the rate of change at which one quantity varies concerning another. This section explains limits with an interesting example, left-hand limit and right-hand limit with solved problems. This section deals with the theorems and prepositions for functions, which are helpful in calculating the limits of some trigonometric functions. Calculus is a branch of Maths dealing with the study of change in the value of a function as the points in the domain change. In this chapter, initially, students gain an intuitive idea of derivative (without actually defining it). Later, the chapter provides a simple definition of a limit and some algebra of limits. Finally, the chapter returns to a description of derivative and some algebra of derivatives.