  We initiate the study of C*-algebras and groupoids arising from left regular
representations of Garside categories, a notion which originated from the study
of Braid groups. Every higher rank graph is a Garside category in a natural
way. We develop a general classification result for closed invariant subspaces
of our groupoids as well as criteria for topological freeness and local
contractiveness, properties which are relevant for the structure of the
corresponding C*-algebras. Our results provide a conceptual explanation for
previous results on gauge-invariant ideals of higher rank graph C*-algebras. As
another application, we give a complete analysis of the ideal structures of
C*-algebras generated by left regular representations of Artin-Tits monoids.
