Wilhelm Schlag turned his notes from a first-year graduate course into a book of sorts. It covers a lot of the topics you listed and it has a bunch of good problems. The bookA manuscript appears on his website here: http://www.math.uchicago.edu/~schlag/bookweb.pdfhttp://www.math.uchicago.edu/~schlag/bookweb.pdf; the published version of the book can be found here: http://www.ams.org/bookstore-getitem/item=gsm-154
Updated with link to the published version of the notes linked
Fixed an outdated link with the current one.
