Explore the fundamental concepts of projective geometry and its applications in differential geometry in this 37-minute video lecture. Delve into the projective view of general conics and their correspondence with 3x3 symmetric projective matrices. Learn about projective linear algebra, distinguishing between projective points as row vectors and projective lines as column vectors. Discover the importance of duality in projective geometry and its absence in most linear algebra treatments. Examine Pappus' theorem and its dual result from this perspective. Investigate the advantages of using projective coordinates to represent points and lines in the plane, including the ability to use integer arithmetic and simplify computations for finding meets and joins. Gain valuable insights into this essential mathematical subject that illuminates various areas of mathematics.