In this introductory chapter, we present some basic material that should be helpful when reading the rest of this book. Therefore, we will often refer to this chapter in the subsequent parts of the text. Although our book is devoted to point processes in reliability (mostly various shock models), the presentation relies also on the notions and some basic properties of the failure rate, the mean residual lifetime, stochastic ordering, etc. Therefore, along with some initial and introductory description of point processes, these topics will be also covered in this chapter. Note that, our aim here is to discuss relevant introductory material rather than to present the basics of reliability theory systematically as it is done in conventional textbooks on reliability.