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This text is based on the class notes of a VLSI signal processing circuit course series (EEE598) the author developed for the EE department at Arizona State University. The materials are organized into nineteen special topics covering various state-of-the-arts symmetry based VLSI circuit design techniques for basic VLSI circuit elements, circuit modules and systems, where the symmetry principle and methods with inherently low PVT sensitivity are used to design VLSI circuits with superior scalability and performance for various VLSI SOC applications.