Here are some places where you can get free access to relevant research and study material.

General

OPEN ACCESS DIGITAL THEOLOGICAL LIBRARY

A great place for finding open access books and articles.

JSTOR

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.

CORE

A large collection of open access research papers.

INTERNET ARCHIVE

Many older books can be read online here.

GOOGLE SCHOLAR

Links to many books and articles.

EPDF

A variety of books available for free downloading; but note that some may be infringing copyright.

TAYLOR AND FRANCIS

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. 

ACADEMIA and RESEARCH GATE

Two free places where people post their research papers.  You can sign up free.

IIUM Journals

Open access journals published by the International Islamic University of Malaysia.  The various journals deal with different academic and professional concerns from an Islamic perspective.   Titles include Intellectual DiscourseIIUM Law JournalInternational Journal of Economics, Management and Accounting, Revelation and Science, and Al-Burhan: Journal of Qur’an and Sunnah Studies. 

Qur'an and Bible

BIBLE HUB

Greek and Hebrew texts, interlinear, translations, concordances, lexicons and some older, popular commentaries.

STEP BIBLE

A range of Bible research tools

JTS TORAH ONLINE

Lots of interesting material from the Jewish Theological Seminary, New York

LOGOS

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.

THEOLOGY ON THE WEB

Links to a number of good online resources on biblical and other Christian theological scholarship

 

ALTAFSIR.COM

Qur'anic commentaries and translations

INTRODUCING THE QUR'AN

Podcasts from Oxford University's Prof Nicolai Sinai

THE QUR'AN SEMINAR

A study of 50 Qur’anic passages with commentaries by different Muslim and non-Muslim scholars.

INTERNATIONAL QUR'ANIC STUDIES ASSOCIATION

Includes a page of useful links to Qur'anic Studies resources and conferences.

DICTIONARY OF QUR'ANIC TERMS

By Mustansir Mir

QUR'ANIC ARABIC CORPUS

The Arabic grammar, syntax and morphology for each word in the Qur'an

THE QUR'AN BETWEEN JUDAISM AND CHRISTIANITY

Recordings of a conference on this theme from a conference at the University of Nottingham, 2016.

Some very interesting material on the study of the Qur'an and the Bible.

Dialogues and intertextual studies 

MINDING SCRIPTURE

Podcasts discussing various aspects of Jewish, Christian and Muslim scriptures, from Notre Dame University

THE BUILDING BRIDGES SEMINARS

Publications from a series of meetings of Muslim and Christian scholars.

SCRIPTURAL REASONING

Muslims, Christians and Jews studying Scriptures together.  The website includes a page of academic papers.