This is a question that comes up frequently. You will do yourself a big favor if you start with \"Epicurus and His Philosophy\" by Norman DeWitt, but below are several links to lists of books and discussions of reading suggestions that are freely available.
There are many controversies as to the proper interpretation of Epicurus. If, instead of starting with DeWitt or the primary sources, you choose to read a modern book written in the last 30 years, you will find Epicurus presented to you from the perspective that Epicurus was primarily interested in \"absence of pain\" rather than \"pleasure.\" That is why many of us at this forum recommend Norman DeWitt's \"Epicurus and His Philosophy\" as a starting point. DeWitt's perspective is found in the opening chapter of his book which can be read for free here. An article - \"Philosophy For The Millions\" - summarizing DeWitt's perspective is here.
As an initial list for a new student of Epicurus start, I would suggest the following, in order of priority:
- \"Epicurus and His Philosophy\" by Norman DeWitt
- The Biography of Epicurus by Diogenes Laertius. This includes the surviving letters of Epicurus, including those to Herodotus, Pythocles, and Menoeceus.
- \"On The Nature of Things\" - by Lucretius (a poetic abridgement of Epicurus' \"On Nature\"
- \"Epicurus on Pleasure\" - By Boris Nikolsky
- The chapters on Epicurus in Gosling and Taylor's \"The Greeks On Pleasure.\"
- Cicero's \"On Ends\" - Torquatus Section
- Cicero's \"On The Nature of the Gods\" - Velleius Section
- The Inscription of Diogenes of Oinoanda - Martin Ferguson Smith translation
- A Few Days In Athens\" - Frances Wright
- Lucian Core Texts on Epicurus: (1) Alexander the Oracle-Monger, (2) Hermotimus
- Philodemus \"On Methods of Inference\" (De Lacy version, including his appendix on relationship of Epicurean canon to Aristotle and other Greeks)
Here is a \"library\" page at NewEpicurean.com with links to where many additional translations are available for free on the internet.
Discussion of this FAQ is here.
Update 10/21/19: Consult this thread for more thoughts on reading list and proper order of approach: Profile of Past Reading
Update 11/21/20: After you have read DeWitt's book, here are additional comments I would make to someone asking where to read next:
Have you read the full bio of Epicurus in Diogenes Laertius which includes all Epicurus' letters? I would be sure to read that so you have it down first hand.
Have you read Lucretius? If you are interested in that then I would stick with the Martin Ferguson Smith edition, which has good footnotes, though there are a couple of sections I have issues with. But overall its the best and most current.
Have you read the Inscription of Diogenes of Oinoanda? The best version of that is on the dedicated website based in Catalonia.
I do also recommend A Few Days In Athens, especially if you read through these criticisms of it. Despite the issues there is still a lot of good material in it, if you can get past the 18th-century flowery language in the opening chapters.
If you are at all interested in the epistemology issues, I highly recommend the de Lacy version of Philodemus \"On Methods of Inference\" but start at the back with DeLacey's commentary before you read any of the text. There is a lot of good material there about how Epicurean epistemology contrasts with the others.
On the right margin of the home page of the EpicureanFriends website you will see the list of a couple of articles in the paragraph entitled \"Don't be a Stoic in Disguise.\" I would first read the Nikolsky and Wentham articles referenced there, and then go for the chapters on Epicurus in \"The Greeks on Pleasure.\" That book (Greeks on Pleasure) is really the monumentally best-researched work that provided the foundation for the Nikolsky article and shows the errors in the \"absence of pain\" argument.
If you want some entertainment as part of your study, be sure to include the works of Lucian of Samosata, especially those listed here. Lucian is not thought of as a totally orthodox Epicurean, but his Epicurean sympathies are clear in these essays.
If those ideas and sequence don't help, please ask on the forum, especially if you have specific areas you want to target first.
Here's a recent (May 2021) discussion of reading lists at the Facebook Epicurean Group.