This book is a collection of most published papers in the idea of certain classes of analytic functions with complex order.This book consists of seven chapters, organized as follows . In chapter 1, we introduce some interesting definitions of univalent and p-valent functions.In chapters 2,3,4, and 5, we introduced and studied some interesting classes of analytic and univalent functions with complex order and obtained numerous sharp results for these classes.In chapter 6 we studied and derived several interesting properties of two classes of analytic functions with bounded boundary rotation and bounded argument with complex order. In chapter 7 we studied and derived several interesting properties of two classes of p- valent functions with complex order.All results obtained in this book are sharp.