This lecture covers the concept of buckling in beams, explaining how an instability occurs when a beam deforms under compression, leading to failure at a load much smaller than the maximum stress. The instructor discusses the two deformation regimes based on the axial load and introduces the Euler model for buckling, highlighting the critical stress and load calculations. Various buckling modes and the importance of choosing the correct axis for rotation are explored, along with the concept of slenderness ratio and the effective length of beams.