The latest book in our successful series IT Revolution in Architecture provides a concise summary of how our perception of the space around us has radically changed in recent years. We could even go as far as to say that we ourselves shape the space around us according to how our perceptions of the universe alter and develop, and mathematics plays a pivotal role. In this book, the "virtual" protagonist of the journey through the concept of space is the square. Michele Emmer, born in 1945, is Professor of Mathematics at the University La Sapienza in Rome and has authored many books and films on the subject of mathematics and art and culture. He was also responsible for exhibitions at the Venetian Biennale and the Cite des Sciences La Villette in Paris.