I have a little hard time understanding the definition of a simply connected space in terms of a fundamental group. A space is simply connected if its fundamental group is trivial, has only one element? It's been some time since I played around with homotopy. My understanding is that a set of path homotopy classes of loops satisfies the axioms of a group. Is one element of that group just one loop? If so, how does that tell you there is no holes the loop is encompassing. This where I get confused. Thanks.