. For the first part of the course I suggest you look at some of the following on-line notes to broaden your viewpoint!
<ul>
<li> <a href="http://homepage.ntlworld.com/ivan.wilde/notes/fa1/">I.F. Wilde's notes</a> Only the first four chapters are really relevant for us and I will proceed a little more slowly.
<li> The coverage of  <a href="http://rutherglen.ics.mq.edu.au/wchen/lnlfafolder/lnlfa.html">WWL Chen</a>'s notes is a bit closer to what we will do<br>
The first two chapters should help you to recall some of 18.100.
<li> Another useful set of notes are those by <a href="http://www.mth.uea.ac.uk/~h720/teaching/functionalanalysis/materials/FAnotes.pdf">T.B. Ward</a> Especially Chapters 1-5, but I will do a bit more on Lebesgue integration.
<li> For integration I will use a heavily modified version of (Jan) Mikusinski's approach which you can find in Debnaith and (Piotr) Mikusinski ``An introduction to Hilbert spaces with applications'' (Academic Press)
<li> A nice reference for Hilbert spaces is G.F. Simmons ``Introduction to Topology and Modern Analysis'' 
<li> You might like to look at P. Halmos' ``A Hilbert space problem book''
<li> A good over-all reference, a little more advanced than this course, is P.D. Lax's book ``Functional Analysis'' (Wiley-Interscience) -- a nice book to have.
</ul>
Notes for the course
<ul>
<li> A version of the notes for you to annotate will go up on <a href="http://nb.mit.edu">nb</a> (under 18.102, but not up yet).<br>
Note that I will continue making changes to some parts of the notes.
<li> <a href="FunctAnal.pdf">Lecture notes </a>(3 February, 2015)</br>
Broken out into chapters:<br>
<a href="Chapter1.pdf">Normed and Banach spaces -- Chapter 1 </a> </br>
<a href="Chapter2.pdf">Lebesgue integration -- Chapter 2 </a><br>
<a href="Chapter3.pdf">Hilbert space -- Chapter 3 </a><br>
<a href="Chapter4.pdf">Applications -- Chapter 4 </a><br>
<a href="Chapter5.pdf">Problems -- Chapter 5 </a><br>
</ul>