In this book we have investigated some newly developed results related to the growth rates of entire functions represented by a vector valued Dirichlet series on the basis of their relative Ritt order and relative Ritt lower order. Also we have studied some growth properties of the entire functions represented by a vector valued Dirichlet series on the basis of relative Ritt type and relative Ritt weak type, some growth rates of composition of entire and meromorphic functions on the base of generalized relative order and generalized relative lower order of meromorphic functions with respect...