Hellenic polytheism - free (and reliable!) resources
The Homeric Hymns: http://www.theoi.com/Text/HomericHymns1.html
The Homeric Hymns, translated by Apostolos N. Athanassakis are also available to read online for free:
https://archive.org/details/homerichymns00home
https://archive.org/details/homerichymns00atha
https://archive.org/details/homerichymns0000unse
The Orphic Hymns: http://www.theoi.com/Text/OrphicHymns1.html
The Orphic Hymns, translated by Apostolos N. Athanassakis: https://archive.org/details/isbn_9780891301196
The Delphic Maxims: https://www.scribd.com/document/186693295/Delphic-Maxims
Many other primary sources from ancient Greece can be found in English translations at theoi.com, which is a fantastic resource for information about the Theoi.
Modern prayers to the Theoi:
Hearthstone: https://greekpagan.com & https://greekpagan.tumblr.com/ Note: downloads of Hearthstone’s two books of Hellenic prayers can be purchased at https://www.etsy.com/shop/HearthfireHandworks
winebrightruby: https://winebrightruby.tumblr.com/devotional
Some of the best and most essential sources to start with - and for continuous reference, in my opinion:
Adam, John. The Religious Teachers of Greece. Clifton, New Jersey: Reference Book Publishers, Inc, 1965. https://www.giffordlectures.org/lectures/religious-teachers-greece
Adkins, Lesley and Adkins, Roy A. Handbook To Life In Ancient Greece https://archive.org/details/handbooktolifein00adki
Betegh, Gabor. Greek Philosophy and Religion. https://www.academia.edu/4990433/Greek_Philosophy_and_Religion
Burkert, Walter. Greek Religion https://archive.org/details/greekreligionarchaicandclassical
Angelos Chaniotis, “The Life of Statues of Gods in the Greek World’” Kernos [Online], 30 | 2017, posted on October 01, 2019. URL : http://journals.openedition.org/kernos/2492 ; DOI : https://doi.org/10.4000/kernos.2492
Dignas, Beate, and Kai Trampedach, eds. 2008. Practitioners of the Divine: Greek Priests and Religious Figures from Homer to Heliodorus.Hellenic Studies Series 30. Washington, DC: Center for Hellenic Studies. http://nrs.harvard.edu/urn-3:hul.ebook:CHS_DignasB_and_TrampedachK_eds.Practitioners_of_the_Divine.2008
Dillon Matthew. “Household, Families and Women” in Kindt, J. Eidinow, E. (eds) The Oxford Handbook of Religion in the Ancient World, Oxford University Press, Oxford, 2015. https://www.academia.edu/7974646/HOME_AND_HEARTH._THE_CLASSICAL_GREEK_EXPERIENCE_OF_DOMESTIC_RELIGION_in_Kindt_J._Eidinow_E._eds_The_Oxford_Handbook_of_Religion_in_the_Ancient_World_Oxford_University_Press_Oxford_2015
Furley, WIlliam D. and Jan Maarten Bremer. Greek Hymns: Selected Cult Songs from the Archaic to the Hellenistic period. Part One: The texts in translation.Tübingen: Mohr Siebeck, 2001. https://www.mohrsiebeck.com/uploads/tx_sgpublisher/produkte/leseproben/9783161586552.pdf
Garrett, Jan. Did Socrates ‘Teach New Deities’? Or: Homer’s Gods, Plato’s Gods http://people.wku.edu/jan.garrett/pgods.htm
Hesiod. Theogany https://www.theoi.com/Text/HesiodTheogony.html
Hesoid. Works and Days https://www.theoi.com/Text/HesiodWorksDays.html
Kearns, Emily. The Nature of Heroines in The Sacred and the Feminine in Ancient Greece edited by Sue Bundell and Margaret Williamson, Routledge, 1998. pp. 96-110. http://isites.harvard.edu/fs/docs/icb.topic1500680.files/kerns%20nature%20of%20heroines.pdf
Kindt, Julia. “Personal Religion: A Productive Category for the Study of Ancient Greek Religion?” The Journal of Hellenic Studies, vol. 135, 2015, pp. 35–50., www.jstor.org/stable/44157346
Kitts, Margo. What’s Religious about the Iliad? Religion Compass 7/7 (2013): 225–233, 10.1111/rec3.12050 Wiley & Sons Ltd., 2013. https://www.academia.edu/5744383/_Whats_religious_about_the_Iliad_Religion_Compass_7_7_2013_225_233_draft_version_
Koutoupas, A. “The Meaning of Reciprocity in Ancient Greek Religion.” https://www.academia.edu/12126893/The_Meaning_of_Reciprocity_in_Ancient_Greek_Religion
Meyer, Marvin.The Ancient Mysteries: A Sourcebook: Sacred Texts of the Mystery Religions of the Ancient Mediterranean World https://archive.org/details/ancientmysteries0000unse_p7i2
Morford, Mark, P.O., Lenardon, Robert J. and Sham, Michael. “The student companion to Classical Mythology, Tenth Edition”: https://global.oup.com/us/companion.websites/9780199997329/
Otto, Walter.The Homeric Gods https://archive.org/details/in.gov.ignca.4448/page/n5/mode/2up
Petrovic, Andrej, and Petrovic, Ivana. “Introduction” in Inner Purity and Pollution in Ancient Greek Religion Vol I. https://www.academia.edu/30262742/Introduction_in_Inner_Purity_and_Pollution_in_Ancient_Greek_Religion_Vol_I
Pirenne-Delforg, Vinciane and and Francesca Prescendi. Feeding the gods? Sacrifice and representation of the divine. https://books.openedition.org/pulg/1604
Rask, K.A. “Devotionalism, Material Culture, and the Personal in Greek Religion.” https://journals.openedition.org/kernos/23
Seznac, Jean.The Survival of the Pagan Gods: The Mythological Tradition and Its Place in Renaissance Humanism and Art, Princeton University Press, 1953. Chapter One, pp. 11-36. http://people.bu.edu/bobl/paganchristian.pdf
Smith, William. A Dictionary of Greek and Roman Antiquities
John Murray, London, 1875. Articles on Greek and Roman religion, including divination, festivals, funerals, magic, priestly officers, and rituals: https://penelope.uchicago.edu/Thayer/E/Roman/Texts/secondary/SMIGRA/Religion/home.html
Von den Hogg, Ralf. “Images and Prestige of Cult Personnel in Athens between the Sixth and First Centuries BC” in Practitioners of the Divine: Greek Priests and Religious Officials from Homer to Heliodorus, edited by Kai Trampedach, and Beate Dignas. Kolloquium. pp 107-141 http://archiv.ub.uni-heidelberg.de/propylaeumdok/2166/1/vdH_Images_Prestige_2008.pdf
Webster, Michael. Reading Hesiod’s Theogany. 2005. https://faculty.gvsu.edu/websterm/Hesiod2.htm
Ways of Interpreting Myths
https://faculty.gvsu.edu/websterm/ways.htm
Weddell, Poly. Touching the Gods: physical interaction with cult statues in the Roman world. http://etheses.dur.ac.uk/555/1/Touching_the_Gods.pdf?DDD3+
Whitmore, Emily. Personal Religion in ancient Greece. https://www.academia.edu/8729313/Personal_religion_in_ancient_Greece
Woodward, Roger D. The Cambridge Companion to Greek Mythology https://archive.org/details/TheCambridgeCompanionToGreekMythology/page/n1/mode/2up
Find more information at my Masterpost of Resources for Hellenic & Roman Polytheism: https://honorthegods.tumblr.com/masterpost
Please feel free to ask me questions or contact me about books/articles on specific topics related to ancient Greek religion and modern Hellenic polytheism!