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


*

*Hatcher - Algebraic Topology (used in last semester's MATH 4204 at ANU)

*Bredon - Geometry and Topology

*Rotman - Algebraic Topology 


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