In this book, we study the existence of fixed points for various types of maps, such as compatible of type (P) maps, compatible of type (P1) maps, compatible of type (P2) maps, compatible of type (A) maps and 2-compatible maps in probabilistic metric spaces. We also investigate the existence of common fixed points in Menger spaces. This book is divided into SIX chapters (excluding Chapter 0). Chapter 1: A fixed point theorem for four self maps in a Menger space using a contractive control function. Chapter 2: A sufficient condition for a sequence, in a Menger space, to be Cauchy. Chapter 3: A fixed point theorem for four self maps in a Menger space under the influence of a contractive control function of type (AS) Chapter 4: A common fixed point theorem in Menger probabilistic metric spaces using compatibility. Chapter 5: A common fixed point theorem in Menger spaces using an implicit relation. Chapter 6: A fixed point theorem in Menger PQM spaces using weak compatibility. Each chapter is almost self contained.