This is one of the most significant periods in European Philosophy. It always starts with Rene Descartes, the first major philosopher to use "modern methods", ie: low reliance on:

  1. The philosophies of Plato and Aristotle (see it's all footnotes to Plato)
  2. Arguments from authority of the Bible (see Medieval Philosophy)

The early modern period is characterised by the battle between Rationalists and Empricists such as:

Issac Newton's theories and a general focus on the scientific method coloured this period. Despite this, most philosophers' arguments relied on introspection which lead to such atrocities (as far as modern philosophers are concerned) as Descartes' homunculi.

Immanuel Kant is usually said to end this period by determining the final limit of skepticism and turning philosophy from metaphysics to language (analytic) and existentialism (continental). It has been said1 that all modern philosophy (or at least all coming out of Germany) is "footnotes to Kant".

1: I am unable to determine the source of this, although it may well be Alfred North Whitehead (see it's all footnotes to Plato). Please msg me with leads!