Neo-Platonism is a Hellenistic school of philosophy founded by Plotinus in the 3rd Century A.D. The term "neo-platonism" itself was not used in ancient times (it was in fact not coined until the early 19th Century), and Neo-Platonists would have considered themselves simply Platonists, although their beliefs demonstrate significant differences from those of Plato.
The Egyptian philosopher Plotinus (along with his lesser-known teacher, Ammonius Saccas), is widely considered the founder of Neo-Platonism, developing his theories initially in Alexandria in his native Egypt, and then later in Rome. He was influenced by the teachings of classical Greek philosophy, but also by Persian and Indian philosophy (from his extensive travels) and Egyptian theology. Although his original intention was merely to preserve the teachings of Plato and Socrates, he effectively fused Platonism (more specifically, Middle Platonism) with oriental mysticism.
Neo-Platonism is generally a religious philosophy, combining a form of idealistic Monism with elements of Polytheism. It teaches the existence of an ineffable and transcendent One, from which emanates the rest of the universe as a sequence of lesser beings (although later Neo-Platonic philosophers added hundreds of intermediate beings such as gods, angels and demons).
Plotinus's student, Porphyry (c. 233 - 309 A.D.), assembled Plotinus's teachings into the six "Enneads". Porphyry was a Syrian Neo-Platonist philosopher, who also wrote widely on astrology, religion, mathematics and musical theory, and was a strong opponent of Christianity and defender of Paganism.
Iamblichus Chalcidensis (c. 245 - 325 A.D.) was another Syrian (and student of Porphyry), who was instrumental in determining the direction taken by later Neo-Platonic philosophy. One of the last major Greek philosophers, Proclus Lycaeus (412 - 485 A.D.), set forth possibly the most elaborate, complex and fully-developed Neo-Platonic systems, even incorporating the ancient Greek gods into the Neo-Platonic hierarchical system. Other important Neo-Platonists include Hypatia of Alexandria (370 - 415 A.D.), the Roman Emperor Julian (c. 331 - 363 A.D.), Hierocles of Alexandria (active around 430 A.D.), Simplicius of Cilicia (c. 490 - 560 A.D.) and Damascius (c. 458 - 538 A.D.), the last teacher of Neo-Platonism at Athens.
Some central tenets of Neo-Platonism (e.g. that evil is merely the absence of good, which comes from human sin) were very influential in St. Augustine of Hippo's development of Christian dogma, although eventually he effectively abandoned Neo-Platonism altogether in favor of a doctrine based more on his own reading of Scripture. The influence of Neo-Platonism on Origen (c. 185 - 254A.D.), as well as on Boethius, John Scotus Eriugena (c. 815 – 877) and St. Bonaventura (1221 - 1274), also proved significant for both the Eastern Orthodox and Western branches of Christianity.
In the Middle Ages, Neoplatonist ideas influenced Jewish thinkers, including Solomon ibn Gabirol (1021 - 1058) and the Kabbalist Isaac the Blind (1160 - 1235), as well as Islamic and Sufi thinkers such as al-Farabi (872 - 951), Avicenna and Maimonides.
There was something of a Neo-Platonist revival during the Italian Renaissance, with such luminaries as Nicholas Cusanus (1401 - 1464), Giovanni Pico della Mirandola (1463 - 1494), Marsilio Ficino (1433 - 1499), Michelangelo (1475 - 1564), Sandro Botticelli (1445 - 1510), the Medici family and, later, Giordano Bruno (1548 - 1600), as well as with the Cambridge Platonists in 17th Century England.