This is a survey on bi-Lagrangian manifolds, which are symplectic manifolds
endowed with two transversal Lagrangian foliations. We also study the
non-integrable case (i.e., a symplectic manifold endowed with two transversal
Lagrangian distributions). We show that many different geometric structures can
be attached to these manifolds and we carefully analyse the associated
connections. Moreover, we introduce the problem of the intersection of two
leaves, one of each foliation, through a point and show a lot of significative
examples.Comment: 30 page
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