Principles of Advanced Mathematical Physics

18 Elementary Group Theory.- 19 Continuous Groups.- 20 Group Representations I: Rotations and Spherical Harmonics.- 21 Group Representations II: General; Rigid Motions; Bessel Functions.- 22 Group Representations and Quantum Mechanics.- 23 Elementary Theory of Manifolds.- 24 Covering Manifolds.- 25 Lie Groups.- 26 Metric and Geodesics on a Manifold.- 27 Riemannian, Pseudo-Riemannian, and Affinely Connected Manifolds.- 28 The Extension of Einstein Manifolds.- 29 Bifurcations in Hydrodynamic Stability Problems.- 30 Invariant Manifolds in the Taylor Problem.- 31 The Early Onset of Turbulence.- References.