Theoretical Fluid Dynamics This textbook gives an introduction to fluid dynamics based on flows for which analytical solutions exist like individual vortices vortex streets vortex sheets accretions disks wakes jets cavities shallow water waves bores tides linear and non linear free surface waves capillary waves internal gravity waves and shocks. Advanced mathematical techniques ( calculus ) are introduced and applied to obtain these solutions mostly from complex function theory (Schwarz Christoffel theorem and Wiener Hopf technique) exterior calculus singularity theory asymptotic analysis the theory of linear and nonlinear integral equations and the theory of characteristics. Many of the derivations so far contained only in research journals are made available here to a wider public. Description of fluids Flows in the complex plane Vortices corner flow and flow past plates Jets wakes and cavities Kelvin Helmholtz instability Kinematics of waves Shallow water waves Free surface waves Existence proof for weakly nonlinear water waves Sound and internal gravity waves Supersonic flow and shocks.