This book is based on the lectures presented at the Special Session on Nonlinear Functional Analysis of the American Mathematical Society Regional Meeting, held at New Jersey Institute of Technology. It explores global invertibility and finite solvability of nonlinear differential equations.

1. Global Invertibility and Finite Solvability 2. Boundary Conditions and Vanishing Index for a-Contractions and Condensing Maps 3. Recent Progress in Symplectic Geometry 4. Solvability of Semilinear Operator Equations and Applications to Semilinear Hyperbolic Equations 5. Some Remarks on Operator-Valued Means 6. Recent Progress in Periodic Orbits of Autonomous Hamiltonian Systems and Applications to Symplectic Geometry 7. Critical Points in the Presence of Order Structures