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In this paper we construct an $\mathcal{A}_\infty$-category associated to aLegendrian submanifold of jet spaces. Objects of the category are augmentationsof the Chekanov algebra $\mathcal{A}(\Lambda)$ and the homology of the morphismspaces forms a new set of invariants of Legendrian submanifolds called thebilinearised Legendrian contact homology. Those are constructed as ageneralisation of linearised Legendrian contact homology using twoaugmentations instead of one. Considering similar constructions with moreaugmentations leads to the higher order compositions map in the category andgeneralises the idea of [6] where an $\mathcal{A}_\infty$-algebra wasconstructed from one augmentation. This category allows us to define a notionof equivalence of augmentations when the coefficient ring is a field regardlessof its characteristic. We use simple examples to show that bilinearisedcohomology groups are efficient to distinguish those equivalences classes. Wealso generalise the duality exact sequence from [12] in our contest, andinterpret geometrically the bilinearised homology in terms of the Floerhomology of Lagrangian fillings (following [8]).

Bilinearised Legendrian contact homology and the augmentation category