Explore the physics of biological membranes in this comprehensive lecture from the "Fluctuations in Nonequilibrium Systems: Theory and Applications" program. Delve into the structure and properties of lipid bilayer membranes, examining surface free energy expressions and different types of curvatures. Learn about the Gauss-Bonnet theorem and its applications in membrane physics. Observe simulations of lipid bilayer membranes and study their fluctuations. Investigate semiflexible polymers, including actin filaments, and their role in cellular structures. Analyze the process of membrane budding and its significance in biological systems. Explore the unique properties of axons and their importance in neural communication. Conclude with an examination of non-equilibrium processes in biological membranes, gaining insights into the dynamic nature of these essential cellular components.