Types, Abstraction and Parametric Polymorphism in Higher-Order Logic

This thesis aims to promote types as a powerful tool for abstraction in the interactive theorem prover Isabelle/HOL. The first contribution is having solved an open question under which criteria types can be defined consistently in Isabelle/HOL. The second contribution is development of Transfer and Lifting, tools providing automation for building libraries of abstract types (subtypes and quotients). They are based on notions of Reynolds's relational parametricity and partial quotients.