This document describes the design of ZIMPOL I, the first Zürich Imaging Stokes Polarimeter. This solar vector polarimeter will mainly be used for observations of the solar magnetic field at high spatial and/or spectral resolution. A brief overview of ZIMPOL I is given in the preface. The scientific requirements are then specified in detail. They lead to an instrument concept which consists of several parts: the optical system, the camera system, the real-time image processing system, and the graphical user interface. Data reduction and analysis of observations recorded with this polarimeter are also dealt with in detail. Prototypes of the modulator package and the CCD camera have been tested at various observatories. Results from these tests are presented and discussed.