This introduction to modern set theory covers the aspects of its two main general areas: classical set theory including large cardinals, infinitary combinatorics, descriptive set theory; and independence proofs starting with Goedel's proof around 1938 followed by Cohen's proof in 1963, whereby Cohen's method of forcing probably had a greater influence on mathematics. The author's primary emphasis is on forcing and large cardinals, but there is a discussion of descriptive set theory and infinitary combinatorics as well. (view table of contents)