This text features a careful treatment of flow lines and algebraic invariants in contact form
geometry a vast area of research connected to symplectic field theory pseudo-holomorphic
curves and Gromov-Witten invariants (contact homology). In particular it develops a novel
algebraic tool in this field: rooted in the concept of critical points at infinity the new
algebraic invariants defined here are useful in the investigation of contact structures and
Reeb vector fields. The book opens with a review of prior results and then proceeds through an
examination of variational problems non-Fredholm behavior true and false critical points at
infinity and topological implications. An increasing convergence with regular and singular
Yamabe-type problems is discussed and the intersection between contact form and Riemannian
geometry is emphasized. Rich in open problems and full detailed proofs this work lays the
foundation for new avenues of study in contact form geometry and will benefit graduate students
and researchers.
