Finite-Part Integrals.- Convolution and Duhamel Integrals.- Laplace and Fourier Transforms.- Review of the Least Square Method.- Vector Identities Used in Aerodynamics.- Reynolds Transport Theorem, Isentropic, Continuity, and Momentum Equations.- Vorticity, and Kelvin's Circulation Theorem.- Velocity Potential.- The Biot Savart Law for Incompressible Fluids.- The Fluid-Structure Boundary Condition.- The Aerodynamic Force for the Steady Incompressible Ideal Flow.- Small Perturbation Theory.- Small Perturbation Acceleration Potential.- Compressible Fluid at Rest.- Compressible Fluid in Motion.- Compressible Fluid in Motion: the Doublet Solution.- Theoretical Aerodynamic Modeling of Wings.- Steady Incompressible Ideal Flow and Modeling of Finite Wings .- Two-Dimensional Unsteady Incompressible Flow.- Harmonic Motion, Reduced Frequency, and Kernel.- The Generalized Aerodynamic Force for the Continuous System.- Finite-Element Time Domain Aeroelastic Equations.- Laplace and Fourier Transformed Discrete Aeroelastic Equations.- The Unsteady Kernel.- Industry Standard Doublet Lattice Implementation.- Structural Dynamics: the Concept of Free Vibration Modes.- From the Structural Mesh to the Aerodynamic Mesh: Splining.- Generalized Aerodynamic Force Matrix and Rational Function Approximation.- Equations of Motion in the Laplace Domain with the Use of Rational Function Approximation.- Stability Analysis in the Laplace Domain.- Linear Time-Invariant Systems and Stability.- Linear Time-Invariant Aeroelastic Systems.- Classical Flutter, State Space Model, and Root Locus.- Introduction to the Concept of Body Freedom Flutter.- An Introduction to Nonlinear Aeroelasticity.- An Introduction to Nonlinear Dynamics.