An Introduction to Stability Analysis of Elastic Structural Systems Introduction A Review of the Common Approaches to Stability Analysis in Structural Engineering A Review of the Energy Criteria of Stability for Finite Degrees of Freedom Systems Conclusions References A Review of Some Functional Analysis Concepts Introduction Metric Spaces, Normed Spaces, and Branch Spaces Finite and Infinite Dimensional Normed Spaces; Equivalence and Nonequivalence of Norms Dense Subsets, Total Bounded, and Compact Spaces Operators Inner Product Spaces-Hilbert Spaces Symmetric Positive, and Positive-Definite Operators and Their Energy Spaces Calculus of Operators and Functionals-Extreme Values of Functionals Generalized Derivatives and Sobolev Spaces References General Stability Analysis of Continuous Elastic Systems Introduction Formal Analysis of Stability The Requirement of the Stability at the Unstressed State for a Physically Acceptable Theory of Stability-The Choice of the Energy Norm Stability Analysis with Respect to the Energy Norm References Equilibrium Stability of Continuous Elastic Structures Introduction Buckling and Stability Analysis of the Undimensional Beam Model Torsional-Flexural Buckling of Inextensible Rods Basic Problems in Stability Analysis of Plates and Shells Tridimensional Elasticity References Buckling of Continuous Elastic Structures Introduction The Structural Continuum-The Generanalysis of Stability The Requirement of the Stability at the Unstressed State for a Physically Acceptable Theory of Stability-The Choice of the Energy Norm Stability Analysis with Respect to the Energy Norm References Equilibrium Stability of Continuous Elastic Structures Introduction Buckling and Stability Analysis of the Undimensional Beam Model Torsional-Flexural Buckling of Inextensible Rods Basic Problems in Stability Analysis of Plates and Shells Tridimensional Elasticity References Buckling of Continuous Elastic Structures Introduction The Structural Continuum-The General Formulation of the Neutral Equilibrium The Additional Internal Work and the Neutral Equilibrium Equation Comparisons with Other Formulations Pure Strains in Curvilinear Coordinates Buckling of Bars Buckling by Torsion and Flexure of Thin-Walled Open Cross Sections Lateral Buckling of Deep Beams Buckling of Shells References Bifurcation or Snapping at the Critical State of Continuous Elastic Structures Introduction Equilibrium Paths of General Nonlinear Elastic Systems Bifurcation of Perfect Systems General Aspects of the Postcritical Behavior of Quasiperfect Structural Systems Some Applications of the Initial Postbuckling Analysis References.