Projective-Differential Geometric Synthesis With Elements of Algebraic Geometry

An Expository Literature Review Presented At Euler Circle Math Talk. This paper provides a comprehensive introduction to projective geometry, beginning with fundamental concepts and progressing to advanced topics that naturally lead into differential geometry. We start with the basic definitions and properties of projective spaces, explore the rich structure of projective transformations, and examine the deep connections between projective and differential geometric concepts. Each theorem is accompanied by rigorous proofs, making this exposition suitable for readers ranging from advanced undergraduates to graduate students in mathematics.