Pre-Socratic philosophy

The Pre-Socratic Greek philosophers were active before Socrates.  The popular usage of the term comes from Hermann Diels' work Die Fragmente der Vorsokratiker (The Fragments of the Pre-Socratics, 1903).The term "Pre-Sokratic", however, had been in use as early as George Grote's Plato and the other companions of Sokrates (1865).

Most of what we know about the pre-Socractic philosophers come from quotations by later philosophers and historians. While most of them produced significant texts, none of the texts have survived in complete form.

The standard reference works in English are:
Gompertz, Theodor 1901. The Greek thinkers: a history of ancient philosophy. Volume 1: the beginnings.  London: Murray.
Guthrie W.K. 1962. A history of Greek philosophy. Volume 1: The earlier presocratics and the Pythagoreans. Cambridge University Press. 

The fundamental idea which motivated most of the presocratics (as they are called) is naturalism. This is the idea that questions about life and the world can be answered without using myths, and that "the natural world is the whole of reality".Jenkins I. 1942, in Runes D.D. The dictionary of philosophy. New York:Philosophical Library, p205. 

With the Greeks we see rational thought and scientific reasoning appear.Guthrie W.K. 1962. A history of Greek philosophy. Volume 1: The earlier presocratics and the Pythagoreans. Cambridge University Press, p1.

 List of philosophers and schools 
 Milesian school
Thales (624546 BC)
Anaximander (610–546 BC)
Anaximenes of Miletus (585–525 BC)
Pythagorean Schools
Pythagoras (582–496 BC)
Philolaus (470–380 BC)
Alcmaeon of Croton
Archytas (428–347 BC)
Heraclitus (535–475 BC)
Eleatic School
Xenophanes (570–470 BC)
Parmenides (510–440 BC)
Zeno of Elea (490–430 BC)
Melissus of Samos (C.470 BC–unknown)
Pluralist School
Empedocles (490–430 BC)
Anaxagoras (500–428 BC)
Atomist School
Leucippus (5th century BC, dates unknown)
Democritus (460–370 BC)
Sophism
Protagoras (481–420 BC)
Gorgias (483–375 BC)
Thrasymachus
Callicles
Critias
Prodicus (465–390 BC)
Hippias (485–415 BC)
Antiphon (person) (480–411 BC)
Lycophron
Anonymous Iamblichi
Diogenes of Apollonia (c.460 BC–unknown)

Other groupings 
Seven Sages of Greece
Solon (c. 594 BC)
Chilon of Sparta (c. 560 BC)
Thales (c. 585 BC)
Bias of Priene (c. 570 BC)
Cleobulus of Rhodes (c. 600 BC)
Pittacus of Mitylene (c. 600 BC)
Periander (625–585 BC)
Aristeas of Proconnesus (7th century BC ?)
Pherecydes of Syros (c. 540 BC)
Anacharsis (c. 590 BC)
Theano (mathematician) (5th century BC, dates unknown)

References

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