A Model Of Type Theory In Cubical Sets With Connections Simon Docherty Abstract: In this thesis we construct a new model of intensional type theory in the category of cubical sets with connections. To facilitate this we introduce the notion of a nice path object category, a simplification of the path object category axioms of v.d. Berg and Garner that nonetheless yields the full path object category structure. By defining cubical n-paths and contraction operators upon them we exhibit the category of cubical sets with connections as a nice path object category, and are therefore able to utilise a general construction of a homotopy theoretic model of identity types from the structure of a path object category in order to give our model of type theory.