  This is a book aimed at graduate students and researchers in symplectic
geometry, based on a course I taught in 2019. The primary message is that the
base of a Lagrangian torus fibration inherits an integral affine structure,
which you can use to "read off" a lot of interesting geometry of the total
space. Topics covered include: action-angle coordinates, symplectic reduction,
toric manifolds, visible and tropical Lagrangians, almost toric systems, Milnor
fibres of cyclic quotient singularities, mutation of polygons, non-toric
blow-up, an almost toric view on Lisca's classification of fillings of lens
spaces, resolutions of cusp singularities, Markov triples and Vianna tori. The
book ends with a short list of open problems. Throughout there is an emphasis
on examples and there are some exercises with solutions.
