The Multivariable Differential Calculus Pre-Collegiate course offered by Stanford University is an advanced mathematics course focused on differential calculus for functions of two or more variables. The topics covered include vectors and vector-valued functions in 2-space and 3-space, tangent and normal vectors, curvature, functions of two or more variables, partial derivatives and differentiability, directional derivatives and gradients, maxima and minima, and optimization using Lagrange multipliers. This course is delivered through Stanford's online learning platform. The curriculum was originally designed to match the Stanford Mathematics Department's curriculum, providing a rigorous and university-level learning experience for students. The course uses the textbook "Calculus: A New Horizon, 6th edition (or later)" as the primary resource for study. The prerequisites for this course are Calculus AB, BC (or Calc I, II) or an equivalent qualification. Therefore, students are expected to have a solid foundation in calculus before enrolling in this course. Upon completion of this course, participants will have a deeper understanding and proficiency in multivariable differential calculus. They will have mastered advanced mathematical concepts and techniques, equipping them for further studies in calculus or related fields. The course instructor is Dr. Margarita Kanarsky, who not only instructs this course but also the other mathematics courses offered in the program. Dr. Kanarsky is associated with the Online High School at Stanford Pre-Collegiate Studies, demonstrating significant experience in online mathematics instruction.