This lecture covers Riemann integration for functions of several variables, focusing on the Cartesian product of closed intervals and the volume calculation for closed blocks. It explains the concept of Darboux sums, upper and lower Darboux integrals, and the integrability of functions. The instructor illustrates the topic with examples and definitions, emphasizing the importance of subdivisions and the interpretation of integrals. The lecture concludes with the criteria for integrability and the interpretation of integrals in two dimensions.