Italian Renaissance architect and theorist Andrea Palladio has been described as one of the most influential designers in Western history. He is famous for his mathematically grounded theories, which use formal and spatial proportions to evoke harmony and beauty. These theories are intrinsic to the design of his country villas, which elevated domestic architecture to the status of a classical Roman temple. This chapter focuses on Palladio’s use of mathematical concepts in his theories and how these are translated through the design process into architecture. The chapter commences with an introduction to his life, including his training, mentorship and research. This is followed by an examination of his design theory and its reliance on various types of proportional relationships. The next section describes ten of Palladio’s country villas constructed between 1542 and 1569. These villas, which are also examined in Part II of this book, are the Villa Pisani at Bagnolo, Villa ThieneVilla Thiene at Cicogna, Villa SaracenoVilla Saraceno at Finale di Agugliaro, Villa Pisani at Montagnana, Villa ZenoVilla Zeno at Cessalto, Villa FoscariVilla Foscari (‘Villa Malcontenta’) in Mira, Villa EmoVilla Emo at Franzolo, Villa BadoerVilla Badoer in Fratta Polesine, Villa Almerico Capra ValmaranaVilla Almerico Capra Valmarana (Villa Rotonda) (‘Villa RotondaVilla Rotonda’) in Vicenza and Villa Valmarana in Lisiera. The chapter concludes by reviewing the results of past research examining mathematics in Palladio’s architecture.