In this talk we shall see a proof of the famous " Hairy Ball Theorem" ( an even dimensional sphere does not admit any continuous field of non-zero tangent vectors). This theorem was first stated by Henri Poincare` in the late 19th century. Later this has been proved using homology theory, differential forms or methods from geometric topology. John Milnor gave a proof solely using elementary multivariable calculus, which was published in American Mathematical Monthly in 1978, and we shall be studying the same in the talk.