  This is the author's PhD Thesis (University of Cambridge, 2014) in its
original form. In the first part, using an invariance result, we compute the
symplectic homology of contact-type energy levels for magnetic systems on
surfaces, provided the energy is very large or very small. In the second part,
which is partially contained in the later paper (Benedetti, Ergod. Theory
Dynam. Syst., 2016), we discuss some rotationally symmetric examples and
establish dynamical convexity for symplectic magnetic flows on low energy
levels.
