Hebrew Bible refers to the common portions of the Jewish and Christiancanons. It is a bias-free term that is preferred to both Tanakh and Old Testament when discussing the text in academic writing. See e.g. section 4.3 of the Style Manual for the Society of Biblical Literature. Hebrew here may refer to either the Hebrew language or the Hebrew people (also known as the Jews who always retained use of the Hebrew language as a spoken langauge in Israel, or as the language of prayer and study in the diaspora) or both.
See also
Tanakh for the history of the Hebrew Bible and its interpretation within the Jewish tradition.
Old testament for the history of the Hebrew Bible and its interpretation within the Christian tradition.
