This course is focused on the foundational principles of stability and equilibrium in solid mechanics, specifically structural and mechanical engineering problems. Topics covered include stability criteria, energy and variational methods, and the elastic buckling of elements such as columns, beams, frames, plates, and shells. The derivation and evolution of stability solutions are presented. Furthermore, the integration of stability theory into both finite element and finite strip methods is discussed. The application of stability theory in design standards, with an emphasis on structural steel and cold-formed steel structures, is also reviewed. A basic understanding of structural analysis and numerical methods are required.