This book provides a comprehensive explanation of the background of functional analysis and its origins. It is divided into three parts. It begins with a careful and inspiring exposition of basic ideas on linear and metric structures. The second part is dedicated to the role of general topological notions in the framework of metric spaces. These two parts help the reader to prepare for the main principles of functional analysis, which are then explained in the third part of the book. At each step, theory is accompanied by important examples and applications. Carefully chosen exercises stimulate the reader to work actively with the text. On the whole, this self-contained and up-to-date book can be very useful not only to the advanced undergraduate or graduate student but also to anybody who wants to systemize their knowledge on the elements of the subject.