This lecture covers the design considerations for pressure vessels, distinguishing between thick and thin wall pressure losses, and their applications in biological systems such as aneurysms and bacterial cells. The instructor explains how stresses induced by pressure affect the structural integrity of vessels, leading to potential failures. Additionally, stress transformations are discussed, highlighting the importance of understanding how stresses change in different directions due to material properties and loading conditions. The lecture concludes with the concept of principle stresses and angles, emphasizing the significance of analyzing stress states to ensure structural stability.