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I'd like to read some papers concerning fundamental groups, for example, papers written to explain some basic facts about homotopy explicitly for undergraduate students.

All the papers I have requires many background knowledge (homology, for example) but I'd a paper for young students.

I know that there are many good books but usually in books we find the theory explained in a row, or in the order just to read and follow. I'd like to start some research on a low level .

Suggestions are welcome. Best wishes.

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    The fundamental group has been a basic tool in the topologist's kit for over a century. All modern research presupposes familiarity with it. If you want to read research papers where the fundamental group is explained, you might consider looking up Poincare's original series of papers introducing it (discussed here: http://www.map.mpim-bonn.mpg.de/Poincar%C3%A9%E2%80%99s_homology_sphere).2012-12-11

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There are many books in Algebraic Topology that discuss the fundamental group without talking about homology (singular/cellular or simplicial). Resources I have used:

  1. Hatcher - Algebraic Topology (used in last semester's MATH 4204 at ANU)
  2. Bredon - Geometry and Topology
  3. Rotman - Algebraic Topology

There is no doing research without going through the basics and slogging it out in understandinh the full theory first.

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    You might try my book "Topology and Groupoids", see http://pages.bangor.ac.uk/topgpds.html, which is the only text in Englisn to give a van Kampen theorem for the fundamental groupoid on a set of base points, and so obtain the fundamental group of the circle.2014-11-28
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I find that most books on algebraic topology make things more difficult for students than seems necessary by not using paths of "arbitrary length" so that the paths under composition form a category, that is composition is associative and each path has a left identity and a right identity. That is one can define a path (of length $r$) for some $r \geqslant 0$ in $X$ to be a map $f: [0,r] \to X$; or to be a pair $(f,r)$ where $r \geqslant 0$ and $f: [0, \infty) \to X$ is constant on $[r, \infty)$.

Second the notion of the fundamental groupoid $\pi_1(X,A)$ of $X$ on a set $A$ of base points was introduced by me in 1967, and has many advantages over the usual fundamental group. See my answer to this question: https://mathoverflow.net/questions/40945/compelling-evidence-that-two-basepoints-are-better-than-one

This tool allows more powerful theorems with in many cases simpler or clearer proofs, and is developed and applied in my book Topology and Groupoids, the 2006 edition of a book published in 1968; this groupoid $\pi_1(X,A)$ is used in no other topology text in English, to my knowledge. See also this downloadable book Categories and Groupoids.