This lecture covers the fundamentals of turbocompressor design, including the structure of a turbocompressor stage, the Euler turbomachinery equation, velocity triangles, energy transformation, rothalpy, compressor design maps, and the impact of updated design maps. The instructor explains the link between Euler equations and thermodynamics, the design process of turbomachinery, and 1D-modeling approaches. The lecture also delves into the significance of velocity magnitude and direction in turbomachinery design, the energy transformation in turbomachinery, and the iterative combination of complex models in the design process.