Explore this lecture where Kasia Pernal from Politechnika Lodzka presents the first part of a two-part series on Reduced Density Matrix Functional Theory at IPAM's Non-commutative Optimal Transport Tutorials. Recorded on March 12, 2025, at UCLA, this 71-minute presentation provides a comprehensive introduction to the fundamental aspects of reduced density matrix functional theory, covering essential definitions, concepts, and theorems. The lecture serves as a foundation for the second part, which will focus on approximate density matrix functionals, various strategies, and their limitations. This presentation is part of the Institute for Pure & Applied Mathematics (IPAM) program on Non-commutative Optimal Transport.