- geometrical and topological methods (involving e.g. homologic or homotopic characteristics like degree, Nielsen number, Morse index)
- linear and nonlinear spectral theory
- particular operators (Urysohn, Hammerstein, superposition operators)
- nonlinear dynamical systems
- partial and ordinary differential equations
- integral equations (also of vector functions)
- Volterra and functional differential equations
- function spaces; in particular, spaces of measurable functions
- positive operators and lattices
- Weyl calculus and noncommutative harmonic analysis
- connections with logic and set theory (axiom of choice, continuum hypothesis)
- nonstandard analysis
- measure and integration theory (also finitely additive measures)
- geometry of normed spaces
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