A Topological Introduction to Nonlinear Analysis

I: Fixed Point Existence Theory.- 1. The Topological Point of View.- 2. Ascoli-Arzela Theory.- 3. Brouwer Fixed Point Theory.- 4. Schauder Fixed Point Theory.- 5. Equilibrium Heat Distribution.- 6. Generalized Bernstein Theory.- II: Degree and Bifurcation.- 7. Some Topological Background.- 8. Brouwer Degree.- 9. Leray-Schauder Degree.- 10. Properties of the Leray-Schauder Degree.- 11. A Separation Theorem.- 12. Compact Linear Operators.- 13. The Degree Calculation.- 14. The Krasnoselskii-Rabinowitz Bifurcation Theorem.- 15. Nonlinear Sturm-Liouville Theory.- 16. Euler Buckling.- Appendices.- A. Singular Homology.- B. Additivity and Product Properties.- References.