The gods
Epicurus shares his beliefs about the gods and the various allegories about the gods that comprised Greek religion. He feels that although he does suspect there are real gods responsible for the earth and our daily existence, he doesn't feel that they ever involve themselves in human life in any way which would interfere with human free will. In other words, they're not really relevant to a practical, honest life; he feels we are using gods to explain our own behavior—so they are symbolic archetypes to Epicurus.
Ataraxia
When Epicurus uses the word that often is translated "happy," or in Greek, ataraxia, he is invoking an idea, using the emotion "happiness" as a metaphor for some other state of consciousness. The state of ataraxia is a lot like the state of Buddhist Nirvana, except that in Epicurus's imagination, ataraxia was categorized by a blissful life of doing what one wants. He feels that bliss comes from the knowledge that a person can attain their goals by right living.
Atoms
Epicurus teaches that the universe is comprised of tiny, imperceptible units of matter, called atoms. That's weird, though, because it was still going to be more than 2,000 years before any human properly discovered the scientific atom. He used this concept to represent his perception of the world on a microscopic level, and his intuition was literally correct. To the modern reader, this prediction is now a symbol of the insight of the human imagination.
The pragmatic motif
Not only is Epicurus consistently proposing practical approaches to classical philosophical problems, he is doing it with the explicit goal of using philosophy as a tool to gain a happier, healthier, balanced life. That means that Epicurus has discovered that the true reason someone would do philosophy is to become happier, and in his writing, it makes this recurring theme: That we should focus on strategically pursuing our desires, but only once we're perceiving the world correctly.
The motif of moderate indulgence
Epicurus is similar to Zen Buddhism, in that both acknowledge that the goal of philosophy is to attain bliss by really paying attention to the present reality, the present moment. But Epicurus has this motif that they do not; he says that shame, religion, and social norms are only powerful to the extent that they control our behavior. In other words, he is completely willing to throw away his standard for "moral goodness." Instead, he advocates people indulging, because if someone does something they shouldn't, nature typically corrects that behavior. (Obviously, this writing would apply to only the vices of his time, and couldn't be applied to something more literally addictive, like drugs).
