We offer, in this first chapter, an overview of this book. The book untangles the mechanism of perfect and imperfect bifurcations based on up-to-date mathematics placing more emphasis on engineering pragmatism than on mathematical rigor. First, fundamental issues of a static problem are advanced. Next, an overview of theoretical tools and concepts is presented. Last, the bifurcation of symmetric systems is overviewed using a series of illustrative examples and photographs of materials and structures, such as soil, sand, kaolin, steel, and honeycomb structure.