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In this thesis a measurement of the high energy $\gamma$-ray flux between 200MeV and 1 TeV with the Alpha Magnetic Spectrometer is presented. The AlphaMagnetic Spectrometer (AMS-02) is a multi-purpose particle detector mountedexternally on the International Space Station.  Although primarily designed for the measurement of charged cosmic rays AMS-02is capable of measuring high energy $\gamma$-rays in two complementary modes.Two independent analyses are presented in this thesis, one for each of the twomodes. The event selection criteria and the associated resolution functions arepresented in detail. The effective area is estimated from a full detectorMonte-Carlo simulation and corrected for the most important differences betweendata and simulation. A full sky model for $\gamma$-rays is constructed fromdiffuse emission predictions and recent $\gamma$-ray source catalogs. Adedicated analysis of Fermi-LAT data is performed to fully enable a detailedcomparison with the AMS result.  The measured flux of $\gamma$-rays is presented for various parts of the sky,including comparisons with Fermi-LAT data and with the constructed model. Theinner galaxy is studied in detail, as an example of a region in which thephoton flux is dominated by diffuse emission. The fluxes of several$\gamma$-ray producing sources, including Vela, Geminga and the Crab pulsar areshown. The Geminga pulsar is studied in detail, revealing its pulsed emissionof $\gamma$-rays in the AMS-02 data, which allows to measure its frequency ofrotation and to estimate its magnetic field strength and age. Finally, AMS-02observed an outburst of the flaring blazar CTA-102 at the end of 2016.

Measurement of High Energy Gamma Rays from 200 MeV to 1 TeV with the Alpha Magnetic Spectrometer on the International Space Station