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Physical responses and effects rarely take place instantly upon exerting external signals. It more or less takes time to transport external inputs, such as material, information, or energy from one place to another. This leads to time delay. Time delay prevails in interconnected systems and networks, which may arise from various sources, including physical transport delay, computation delay, and signal transmission delay. In this chapter, we give a number of motivating examples ranging from classical mechanical systems to contemporary biological studies. Along with this introduction, we also provide a concise survey into the literature most relevant to the topics of this book.