Isaac Newton, one of the greatest scientists and mathematicians in history, created the concept of the vector by conceiving forces as vector entities. In his masterpiece Philosophiae Naturalis Principia Mathematica, using these vector concepts, Newton demonstrated that the existence of a gravitational force results in the motion of planets around the Sun, as well as the motion of the Moon around the Earth.  The true nature of this gravitational force, as well as the creation of the universe itself, remains a mystery. This is why the book cover depicts the spectacular opening scene of Stanley Kubrick's cinematic masterpiece 2001: A Space Odyssey, a film that explores, among other issues, ideas about human evolution and the enigma of creation. Mathematics, and particularly vector calculus, is the fundamental scientific tool that allows us to explore the origin and evolution of space and time, as well as the origin of gravity, electromagnetism, and nuclear forces. Some features of the 6th international edition: Radically revised design. The modern new structure of the book highlights its pedagogical features, making the text more concise, reader-friendly, and accessible. Addition of new exercises. The basic concepts of the theory are supported by more practical exercises to facilitate their assimilation. Upgraded illustration. The quality of the figures has been significantly improved, especially for the fundamental three-dimensional figures, to better clarify the basic concepts of the theory.