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Hatcher's book Algebraic Topology is a standard text in the subject, and I was wondering if there were any lecture notes or even syllabi to accompany it. I am mostly concerned with sequencing, meaning the most useful order for a reader to go through the book the first time. Any additional resources for one going through Hatcher would also be welcome, like hints on exercises. Ideally this would be for a more elementary course in algebraic topology, although I have already completed from lecture 24 on of "introduction to Algebraic Topology" lectures by N. J. Wieldberger (found on youtube), and so I have had a basic foundation in some of the concepts, however this seems at a much lower level than Hatcher.

EDIT: I found MIT's Algebraic Topology and it is a good example of what I am looking for. This one focuses on the homology and cohomology sections of the book, and excludes the homotopy sections. I was looking for more like it, but perhaps focusing on other parts of the book?

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    $\begingroup$ For the sequence specifically, you can read through the book as given. The main points to note are that the book starts incorporating homological algebra (and uses it throughout) in Chapter 2, and the appendices of chapters can be skipped temporarily if you want. The last chapter in particular has a series of appendices that are very interesting and worth reading, but are almost like a survey of some more advanced idea from obstruction theory, fibrations, K-theory, etc. $\endgroup$ – anomaly Dec 7 '15 at 22:59
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Here are some typed up lecture notes from a few people:

$\textbf{1. Arun Debray}$

https://www.ma.utexas.edu/users/a.debray/lecture_notes/

He has course notes for a large selection of courses. In particular, for algebraic topology: https://www.ma.utexas.edu/users/a.debray/lecture_notes/215b_notes.pdf

follows Soren Galatius' course found at: http://math.stanford.edu/~galatius/215B15/

$\textbf{2. Evan Chen}$

http://www.mit.edu/~evanchen/coursework.html

He has notes for various courses. In particular, his algebraic topology notes (which don't follow Hatcher) seem to be at a more elementary level:

http://www.mit.edu/~evanchen/notes/SJSU275.pdf

$\textbf{3. Akhil Mathew}$

http://math.harvard.edu/~amathew/notes.html

He has notes for algebraic topology here: http://math.harvard.edu/~amathew/ATnotes.pdf which seems to follow http://isites.harvard.edu/icb/icb.do?keyword=k73000

$\textbf{4. Zev Chonoles}$

http://math.uchicago.edu/~chonoles/expository-notes/

He has notes for Benson Farb's AT class (in fact, you may look at Farb's notes by pressing the "+")

$\textbf{5. Kiyoshi Igusa}$

http://people.brandeis.edu/~igusa/Courses.html

Has lecture notes to courses he taught. In particular, there's an algebraic topology course here:

http://people.brandeis.edu/~igusa/Math121b/Math121b.htm

(there are homotopy theory notes too)

$\textbf{6. Anton Geraschenko}$

http://stacky.net/wiki/index.php?title=Course_notes

Lots of notes for various Berkeley classes (algebraic topology included).

$\textbf{7. Alvin Jin}$

https://people.ucsc.edu/~anjin/AT.pdf

I've begun typing up notes for various things. Assuming I don't get lazy there will be a good number of things.


Other people of interest for other courses/topics (while I'm at it):

$\textbf{1. Keith Conrad}$

http://www.math.uconn.edu/~kconrad/blurbs/

Lots of nice notes.

$\textbf{2. Brian Conrad}$

http://math.stanford.edu/~conrad/

Lots of nice lecture notes (if you click on his courses and click on "handouts")

$\textbf{3. Moor Xu}$

https://math.berkeley.edu/~moorxu/oldsite/

Some course notes typed up.

$\textbf{4. Robert Ash}$

http://www.math.uiuc.edu/~r-ash/

Nice set of books with solutions provided.


I might add more later as they come to mind...

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  • $\begingroup$ What a fantastically thorough answer. $\endgroup$ – Sammy Black Dec 5 '15 at 20:34
  • $\begingroup$ Eva Belmont also has class notes: math.mit.edu/~ebelmont $\endgroup$ – darij grinberg Dec 7 '15 at 22:51
  • $\begingroup$ +1 All wonderful lecture notes and they're all part of my website,where I've attempted to compile as complete a link list of mathematical lecture notes as is currently available on the web. My website can be found at tuloomath.com. Tell anyone you know. $\endgroup$ – Mathemagician1234 Jan 3 '16 at 4:08

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