This chapter presents an overview of the Book Series inDirect Methods, Inverse Methods and Uncertainty Modeling (of which its Volume I: Model-Based and Signal-Based Inverse Methods has already been published), and a presentation of the current Volume II: Fundamental Concepts and Models for the Direct Problem. The chapter includes an introduction to the different topics in Optimization and Identification Techniques detailed in Volume I, and an introduction to topics related to materials, technologies, and discrete modeling, comprising the several chapters included in this Volume II of the Book series. 1 Book Series in Discrete Models, Inverse Methods, & Uncertainty Modeling in Structural Integrity: overview The Book series in "Discrete Models, Inverse Methods, & Uncertainty Modeling in Structural Integrity" is an initiative of the Post-Graduate Program -Integrity of Engineering Materials (PPG-Integridade) of University of Brasilia (UnB), organized as a collaborative work involving researchers, engineers, scholars, from several institutions, universities, industry, recognized both nationally and internationally.