MyLibrary is a very rudimentary .epub, .pdf and .txt reader, but is THE native ebook reading app on the ASUS Transformer. From postings on xda developer's forums, it is undergoing fixes/enhancements and should be updated in the near future (hopefully no later than June 2011
).
I like the look and feel of this app especially the two column layout in landscape mode for .epub ebooks (however, that is not yet available for .pdf ebooks
).
It displays the ebooks elegantly and even has TTS, but lacks TOC and good navigation controls as well as system settings that can be changed. I like to tinker and it doesn't let me...
Other ebook readers you can try are Alkido, Cool reader, FBReader, Moon+ reader as well as the Kindle or Kobo android apps. Just search the Android Devices forum here at mobileread.com for more on these.