This book aims to make Galileo Galilei (1564-1642) accessible to the modern reader by refashioning the great scientist's masterpiece "Discourses and Mathematical Demonstrations Relating to Two New Sciences" in today's language. Galileo Galilei stands as one of the most important figures in history, not simply for his achievements in astronomy, physics, and engineering and for revolutionizing science and the scientific method in general, but also for the role that he played in the (still ongoing) drama concerning entrenched power and its desire to stifle any knowledge that may threaten it. Therefore, it is important that today's readers come to understand and appreciate what Galilei accomplished and wrote. But the mindset that shapes how we see the world today is quite different from the mindset -- and language -- of Galilei and his contemporaries. Another obstacle to a full understanding of Galilei's writings is posed by the countless historical, philosophical, geometrical, and linguistic references he made, along with his often florid prose, with its blend of Italian and Latin. De Angelis' new rendition of the work includes translations of the original geometrical figures into algebraic formulae in modern notation and allows the non-specialist reader to follow the thread of Galileo's thought and in a way that was barely possible until now.