Section 1 Introduction to Stability and Bifurcation in Dynamical Systems and Fluid Dynamics. - Section 2 The Center Manifold Theorem. - Section 2A Some Spectral Theory. - Section 2B The Poincaré Map. - Section 3 The Hopf Bifurcation Theorem in R2 and in Rn. - Section 3A Other Bifurcation Theorems. - Section 3B More General Conditions for Stability. - Section 3C Hopf's Bifurcation Theorem and the Center Theorem of Liapunov. - Section 4 Computation of the Stability Condition. - Section 4A How to use the Stability Formula; An Algorithm. - Section 4B Examples. - Section 4C Hopf Bifurcation and the Method of Averaging. - Section 5 A Translation of Hopf's Original Paper. - Section 5A Editorial Comments. - Section 6 The Hopf Bifurcation Theorem Diffeomorphisms. - Section 6A The Canonical Form. - Section 7 Bifurcations with Symmetry. - Section 8 Bifurcation Theorems for Partial Differential Equations. - Section 8A Notes on Nonlinear Semigroups. - Section 9 Bifurcation in Fluid Dynamics and the Problem of Turbulence. - Section 9A On a Paper of G. Iooss. - Section 9B On a Paper of Kirchgässner and Kielhöffer. - Section 10 Bifurcation Phenomena in Population Models. - Section 11 A Mathematical Model of Two Cells. - Section 12 A Strange Strange Attractor. - References. Language: English