What are the major neoclassical themes in Alexander Pope's An Essay on Criticism?

Rules are very important for Pope, as they were for neoclassicists in general. In An Essay on Criticism he is anxious to argue quite strongly that following the appropriate rules is conducive to good writing. The target audience of the Essay was very small, consisting of a tiny, well-bred readership drawn largely from the upper classes. If one wished to communicate something of lasting significance to this self-selecting literary elite, then it was thought necessary to speak to them in a language they could understand. There was no place in the world of the eighteenth-century English salon or literary coterie for anything that smacked of eccentricity or overt individuality; to ignore this basic prohibition was considered incredibly rude and ill-mannered.

In part 1 of the Essay, Pope further stresses the importance of following human nature not just in writing, but in any kind of creative endeavor. In common with most people at the time, Pope tended to look upon human nature as fixed. Accordingly, writers must endeavor to express human nature in all its universality. Among other things, this approach would ensure that creative works such as poems and novels would endure long after they were written. As they were concerned with the universal and the general, rather than the particular and the specific, they were able to speak clearly to each successive generation.

If writers wish to convey universal truths in their work, they could do a lot worse, says Pope, than to follow the shining example set by their great forebearers of antiquity such as Cicero, Quintilian, and "The Stagirite," namely, Aristotle. These men have spoken to successive generations, and continue to do so, precisely because they dealt so skillfully with human nature. Therein lies their contemporary relevance.

As a highly skilled poet himself, Pope understands that the poetic temperament often instinctively rebels against specific rules and the formal constraint they impose. This, he feels, is a mistake. The great poets of the past understood the necessity of buckling under the rules bequeathed to them by their predecessors. Indeed, if they had not, then Pope would not be in a position to enjoin the current generation of writers to follow their example.

An Essay on Criticism by Alexander Pope encapsulates the Neoclassical literary theories of eighteenth-century England, a period sometimes referred to as "Augustan" for the way writers self-consciously imitated the classical writers of Rome during the period of Augustus, especially Horace.

The first typically Neoclassical theme is the reverence for the great writers of the past. Rather than valorizing originality or eccentricity, Pope advocates synthesizing meticulous craftsmanship with universal and rationally discoverable intellectual and human truths. He sees human nature and the natural world as part of a vast, ordered cosmos with a divine creator and sees all great art as echoing that universal divine order. What makes the ancient poets great for Pope, and defines the impetus behind the Neoclassical emulation of them, is precisely their universality. Poet phrases this eloquently in the lines:

But when t’ examine ev’ry part he came,
Nature and Homer were, he found, the same. ...
Learn hence for ancient rules a just esteem;
To copy Nature is to copy them.

Next, Pope admires balance and symmetry in all aspects of poetry, with the poetic form suited to the subject matter and the language clear and natural, as opposed to technical and contorted, as he thought the case with the Metaphysical poets. 

Another major Neoclassical element in the poem is its satiric genre. Satire was the mode par excellence of Augustan poetry, using wit to deflate the pretensions of what the Augustans saw as radical innovations and grandiose posturing. 

What are Alexander Pope's main concerns in "An Essay on Criticism" epigrams?

An epigram is a short statement similar to making a point in prose, but it is used specifically in verse.

An epigram is a brief, clever, and usually memorable statement.

Although it was Greek in nature, and became its own genre in the Hellenistic period, it is a form adopted by many authors over time to make a point, but in poetic form.

These original epigrams did the same job as a short prose text might have done, but in verse.

Alexander Pope was well know for using epigrams in his verse. Pope make use of this device in "An Essay on Man," and "An Essay on Criticism."

"An Essay on Criticism" is directed not to the reader, but to the would-be critic.

It is written in a type of rhyming verse called heroic couplets.

Not only does this piece provide the budding critic with sound advice as well as criticism, it also provides an insight into the "chief literary ideals of Pope's age."

One epigram notes that often mistakes are singularly made, affecting only the individual, but mistakes take on enormous ramifications when placed in verse.

A Fool might once himself alone expose,
Now One in Verse makes many more in Prose.

This is his first warning, for the epigrams in this piece deal primarily with advice for the would-be critic, along with warnings and pointers. Another epigram notes that it is hard to find genius in poets, but rarer still to find a critic with good taste. Here Pope sets his sights specifically on the critic.

In Poets as true Genius is but rare,
True Taste as seldom is the Critick's Share;

Another example is Pope's advice regarding poets and critics, and who should "judge" and teach others. He states that poets and critics are inspired from the same place: Heaven. Those who would judge, write and teach must prove themselves able by excelling themselves, being good writers. For without the ability to do these things well, one cannot hope to justly or accurately judge the efforts of others.

Both must alike from Heav'n derive their Light,
These born to Judge, as well as those to Write.
Let such teach others who themselves excell,
And censure freely who have written well.