Abstract
Many complex valued functions we encounter are entire functions. In order to classify such functions, maximum modulus function is introduced to measure the growth of an entire function. Naturally, minimum modulus function is also being defined and studied. In fact, the maximum and minimum moduli funcitons are closely related in some cases. The classical Wiman's theorem gives us an affirmative answer for all the entire functions of order strictly less than one. How about the meromorphic functions? What are the relationships between the maximum and minimm moduli of a meromorphic function? We will provide some partial answers in this thesis.