This lecture covers the concept of polymer molecular weights and weight distributions, emphasizing the variability in polymer molecules due to statistical variations in the polymerization process. The instructor explains the importance of both average molecular weight and molecular weight distribution in characterizing a polymer. Various techniques for measuring polymer molecular weights, such as number-average and weight-average molecular weights, are discussed. The lecture also delves into the impact of molecular weight on properties like mechanical strength and processability, highlighting the trade-offs involved in selecting the desired polymer molecular weight.