Here are some places where you can get free access to relevant research and study material.
A searchable broad collection of journal articles and other material you can read online. You can also get a limited number of free downloads per month.
A large collection of open access research papers.
Many older books can be read online here.
Links to many books and articles.
A variety of books available for free downloading; but note that some may be infringing copyright.
This publisher has many relevant books. If you sign up for a free account, you can download 'previews' of many books. These include the contents pages and often the introduction or first chapter of the book.
Two free places where people post their research papers. You can sign up free.
Qur'an and Bible
Greek and Hebrew texts, interlinear, translations, concordances, lexicons and some older, popular commentaries.
A range of Bible research tools
Lots of interesting material from the Jewish Theological Seminary, New York
Bible study books and materials. You can download a free package, although note that some of the material is dated or comes from a very particular perspective. Additional material needs payment.
Links to a number of good online resources on biblical and other Christian theological scholarship
Qur'anic commentaries and translations
Podcasts from Oxford University's Prof Nicolai Sinai
A study of 50 Qur’anic passages with commentaries by different Muslim and non-Muslim scholars.
Includes a page of useful links to Qur'anic Studies resources and conferences.
By Mustansir Mir
The Arabic grammar, syntax and morphology for each word in the Qur'an
Dialogues and intertextual studies
Podcasts discussing various aspects of Jewish, Christian and Muslim scriptures, from Notre Dame University
Publications from a series of meetings of Muslim and Christian scholars.