This chapter provides results on the modeling and verification of systems using transition systems. The goal is to provide the basic fundamental and conceptual theories, which support Event B approach. The chapter explains how invariant properties and safety properties are defined in the framework of a transition system, which may model a program, an algorithm or a distributed system. It details the Event B language and related concepts such as events, contexts, machines and refinement. The chapter explains proof obligations (POs) generated for checking the consistency of the Event B structure. It develops three case studies, in order to illustrate the incremental and proof-based modeling using Event B. The chapter emphasizes the notion of proof-based patterns applied for the Event B method. It describes available tools for supporting the Event B modeling language concludes with the current and future trends for this method.