In the first part of this thesis, we generalize the notion of a Jacobi bracket on the algebra of smooth functions on a manifold to the notion of a Jacobi bracket on an abstract commutative algebra. We also prove certain useful properties of the Jacobi structure on a contact manifold. In the second part of this thesis, we develop a de Rham model for stratified spaces resulting from contact reduction. We show that the contact form induces a form on the quotient, and investigate the properties of the reduced contact form. We also describe a Jacobi bracket on the algebra of 0-forms on the singular contact quotient.