This chapter provides an in-depth exploration of the foundational elements that shape federated learning. It begins with an overview of its key components and workflow. The chapter then explores federated algorithms, highlighting essential techniques such as Federated Averaging. It also highlights their role in optimizing communication efficiency and training performance. Next, it addresses the challenges relating to federated learning. Then, the chapter examines the threats faced by federated learning systems. By presenting these core concepts, this chapter serves as an in-depth guide to understanding federated learning core concepts.