After the death of Plato, his Academy lived on, and there were many revivals of Platonism—and, indeed, there will always be many revivals of Platonism, at least if one notices the patterns in history. Among these revivals, there was the neo-Platonic school of thought, of which Plotinus is the most well known advocate. Often neo-Platonists believed that they were explaining just how Aristotle's own work is related to that of Plato (though clearly giving pride of place to Plato). In his Enneads, Plotinus expresses a broad cosmology, drawing all of experience (often using Platonic, Aristotelian, and Stoic notions) into relation to the "One" from which all reality emanates.

Plotinus was well known for his kindness, and the Enneads is a testimony to his contemplative grandeur. Through direct and (mostly) indirect paths, Plotinus would come to influence all of later Western philosophy. The most important conduits for neo-Platonic thought (though there were others) into the Middle Ages were Augustine of Hippo and the unknown maybe-Syrian-monk Pseudo-Dionysius the Areopagite. These two thinkers would be authorities to the Middle Ages, transmitting much neo-Platonism. Pseudo-Dionysius the Areopagite was particularly deep in his neo-Platonism, though his influence paled in comparison to that of Augustine, who was an uncontested father of early Christianity in the Latin West.

As a short side-note, Pseudo-Dionysius the Areopagite is so-called because of his claim to be a certain Dionysius the Areopagite who was converted by St. Paul. Later thinkers came to realize that he could not be such a person. He clearly drew on the work of Proclus, an exponent of neo-Platonism and could not have lived at the time of Paul of Tarsus. Thus, one pre-appends "pseudo" to his name.

The term "metaphysics" literally means "after physics." It is attributed to a work of Aristotle which, properly speaking, does not have that name given to it by its author. It deals with the problem of "being as such." For this question, we do not need to understand the details of this difficult treatise. Instead, it is enough for us to know something about the history (or at least theories concerning the history). The Metaphysics received its name really for two reasons.

On the one hand, it is the text that is to be studied after Aristotle's Physics. The Physics studies changeable being (or "mobile being", as later medieval writers interpreted Aristotle). The Metaphysics goes beyond this—it studies "being as such" or "being insofar as it is being [i.e. not merely mobile].

On the other hand, the name Metaphysics may well be derived from the fact that one of Aristotle's later followers, Andronicus of Rhodes, happened to organize Aristotle's works such that the text called the Metaphysics came after the Physics.

Really, both explanations can go together. Only one option has been provided that explains this phenomenon. (Be careful not to pick the option that says that the Metaphysics was named for its place within the various physical sciences!)

Plato wrote many dialogues on a great number of philosophical topics. His philosophical genius was matched only by his great stylistic ability to craft dialogues among various interlocutors. The Republic is his great work on political philosophy, one that is read by many people and would be a foundation text (whether accepted or rejected) for much of European political thought through the ages. This lengthy text deals with problems of justice, the way that various classes in a city should interact, how the city reflects the inner life of the human soul, and many other topics. Like much of Plato, the work is very airy and lacks the pragmatism that one finds in his student Aristotle's work The Politics. Nevertheless, the Republic remains an important work of political thought, working through numerous topics pertinent to the civic order—always with the deft expression that one expects from the able pen of Plato.

Sextus Empiricus actually presents us with a quite developed account of what was known as Pyrrhonian Skepticism. The word "skeptic" has a kind of negative connotation, as though the skeptical person really doesn't care about the truth. This is not really what it meant in Greek thought, however. The skeptic doubted that we could come to know anything absolutely. Sextus held that one could always settle for either side of an argument. He defended this position by presenting various "modes" of arguing that show this fact. 

The skeptic was really someone who "kept looking." The Greek roots for the word indeed reflect this outlook, for it means "to think" or "to consider." The Skeptic is someone who does not stop thinking or considering a given matter.

If you pick up any Latin philosophical or theological work from the mid-13th century onward (all the way through early modernity), you will find many references to philosophus or "The Philosopher." This refers to Aristotle, whose philosophical works in the Middle Ages were of utter importance to the development of much of medieval thought. Although many medieval thinkers combined Aristotle's thought with that of others, his corpus was the sine qua non of education during this period of history. It shaped much of Western thought, and it cannot be overestimated how much it shaped the curriculum of learning all the way through the time of early modernity.

The followers of Aristotle were called the "peripatetics", and often his general "school" of philosophy is called "peripatetic" or "peripateticism." This name comes from the one of two sources. On the one hand, his school in Athens had colonnades in which the instruction perhaps occurred. The Greek for "colonnade" is peripatoi. On the other hand, however, it is also said that Aristotle walked while lecturing. The word for "a walker" in Greek is peripatetikos. Hence, he would walk back and forth with his students, lecturing. From this one little habit (or, perhaps, the aforementioned colonnades), there arose a title that was affixed to philosophers for over two millennia!

It is said that Saul of Tarsus was an early convert to Christianity after having a major conversion experience on the way to Damascus. He was an active persecutor of the early followers of Jesus. Upon his conversion, he changed his name to Paul and was a very active member of the young Christian community. In the course of his many travels throughout the Mediterranean, he penned a number of letters that would have incalculable influence on the future of Western thought. Even to this day, secular thought has changed in the West due to the many influences exerted by Paul's epistles. Not only are the ideals of Catholicism and Orthodoxy influenced by Paul; Protestantism in all of its varied forms has a deep and lasting debt to his epistles, the theology of which was very influential on early Protestant thought. From the Enlightenment onward, it became very normal to see Paul as a kind of "perverter" of the primitive message of Jesus. Even where Paul was rejected, these later thinkers were still working within a framework that was defined by many of his insights—whether or not those thinkers realized it in their reactions. 

Among the epistles that are almost certainly of Pauline origin, the following are generally included: Romans, First and Second Corinthians, First Thessalonians, Galatians, Philippians, and Philemon. Other epistles, traditionally attributed to Paul, are debated among modern scholars, who believe that they may have been written by others who wrote under Paul's name. These letters are Second Thessalonians, Colossians, Ephesians, First and Second Timothy, and Titus.

Even for one who is purely secular in his or her outlook, a surface-level knowledge of Paul's writing is essential for understanding a major and important vein of the Western intellectual heritage.