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In mathematical field of complex analysis, value distribution theory deals with the study of density of points in the complex plane at which an analytic function takes a prescribed value. The study of value distribution theory was started about a hundred years ago. By the turn of the century, Borel had succeeded in combining and improving results of Picard, Poincare and Hadamard in such a way that this theory began to takes its shape. In 1926, Rolf Nevanlinna succeeded in creating a far-reaching value distribution theory for meromorphic functions which includes the theory of entire functions as a special case. In 1930, Jovan Karamanta introduced a new class of functions called slowly changing functions which have since been applied in various fields of mathematics. The present book deals with the growths of entire functions with the effect of slowly changing functions.