"ESRF data file (EDF) used as a container to store text and binary data; contains header information and associated binary data; used in a few scientific research applications to store collections of images."
Mathematica has several 3D formats which have various ability as to Import and Export. EDF is supported
Look for the Help button on any notebook, click it, in the search box type "EDF", and click go. It will give you instructions and examples. The following command is also useful:
In[1]: $ImportFormats
I've never worked with HDF "a format that stores series or collections of images". You may need to open the app that created the .edf and save as an alternate format (lower version of edf, or as HDF), if Mathematica cannot read the .edf.