Which of Plato's Dialogues should I read to learn about Socrates' views relevant to the philosophy science and epistemology? I'm quite a beginner in these things and the titles of the Dialogues are hardly helpful.
The Republic is supposed to be Plato's primary work on epistemology.
Also, take a look here: http://en.wikipedia.org/wiki/Platonic_epistemology
As for science, Plato rejected empiricism as a means of gaining knowledge, unlike Aristotle whose ideas contributed greatly to the philosophy of science.