Nonlinear Functional Analysis

Spectral Theory of Bounded Operators:
Self - Adjoint Operators.
Compact Operators.

Fundamental Theorems of Nonlinear Functional Analysis:
Baire Theorem.
Open Mapping Theorem.
Implicit Function Theorem.
Bifurcation Theorem.

Topological Methods:
Brouwer Fixed Point Theorem.
Topological Degree.
Monotone Operators.

Variational Methods:
Ekeland Variational Principle.
Mountain Pass Theorem.
Saddle Point Theorem.