Explore the foundations of differential geometry in this introductory lecture. Delve into classical curves, starting with lines and conic sections before progressing to advanced curve-generating techniques like the Conchoid and Cissoid constructions. Discover the applications of differential geometry in fields such as manufacturing, video game design, robotics, and physics. Gain insights into the connections between differential geometry and other mathematical disciplines, including classical geometry and algebraic topology. Prepare for a unique perspective on the subject, suitable for advanced undergraduates, with opportunities to contribute to new directions in the field.