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This paper begins a series in which we examine the structures of distant galaxies to directly determine the history of their formation modes. We start this series by examining the structures of   z  F850LP  &lt; 27  galaxies in the  Hubble Ultra‐Deep Field  (UDF), the deepest high‐resolution optical image taken to date. We investigate a few basic features of galaxy structure using this image. These include: (1) the agreement of visual eye‐ball classifications and non‐parametric quantitative (CAS, Gini/ M  20 ) methods; (2) how distant galaxy quantitative structures can vary as a function of rest‐frame wavelength; and (3) the evolution of distant galaxy structures up to  z ∼ 3. One of our major conclusions is that the majority of galaxies with   z  850  &lt; 27  are peculiar in appearance, and that galaxy assembly is rapidly occurring at these magnitudes, even up to the present time. We find a general agreement between galaxy classification by eye and through quantitative methods, as well as a general agreement between the CAS and the Gini/ M  20  parameters. We find that the Gini/ M  20  method appears to find a larger number of galaxy mergers than the CAS system, but contains a larger contamination from non‐mergers. We furthermore calculate the merger rate of galaxies in the UDF up to  z ∼ 3, finding an increase with redshift as well as stellar mass, confirming previous work in the  Hubble Deep Field . We find that massive galaxies with   M  *  &gt; 10 10  M ⊙   undergo  4.3 −0.8  +0.8   major galaxy mergers at  z  &lt; 3, with all of this merging occurring at  z  &gt; 1.

The structures of distant galaxies – I. Galaxy structures and the merger rate to z ∼ 3 in the Hubble Ultra‐Deep Field