Dive into the fundamentals of first-order convex optimization in this comprehensive lecture by Praneeth Netrapalli. Explore gradient-based optimization techniques, including gradient descent and Nesterov's accelerated gradients algorithm. Examine the complexity of implementing oracles and optimization processes, and delve into key theorems, proofs, and lower bounds. Gain insights into smoothness concepts and estimate sequences. Analyze rearrangements, telescopic sums, and crucial observations to deepen your understanding of convex optimization principles. Perfect for advanced graduate students, postdocs, and researchers in theoretical physics and computer science seeking to enhance their knowledge of machine learning and statistical physics applications.