Explore advanced concepts in geometric measure theory through this lecture on regularity theory for area-minimizing currents. Delve into topics such as zero forms, dual continuous functions, currents with finite mass, and the chain rule. Examine n-dimensional currents, normal currents, and integral rectifiable currents. Investigate weak convergence, subclasses, n-dimensional caverns, and the closure theorem. Analyze the boundary rectifiability theorem and parametric inequality. Gain insights from experts C. De Lellis and E. Spadaro from the University of Zurich and Max Planck Institute for Mathematics in Leipzig as part of the School and Workshop on "Geometric Measure Theory and Optimal Transport" organized by ICTP Mathematics.