Lecture 1

The topics covered in Lecture 1 were: the "big questions" like "P ?= NP", "P ?= PSPACE", "P ?= LOGSPACE", "SC ?= NL", "P ?= NC", "EXP ?$\subseteq$ P/poly", and "P ?= BPP"; search vs. decision problems and languages; the multitape Turing Machine model; the Extended Church-Turing Thesis; Linear Speedup Theorem; and the classes TIME($f(n)$), SPACE($f(n)$), P, PSPACE, and L (aka LOGSPACE).

If you need a refresher on basic stuff such as the Turing Machine Model (the details of which are as finicky as they are ultimately boring) you might look at Chapter 1 of the Arora-Barak book.