In an undergraduate Abstract Algebra class, it appears that there are two standard approaches: "groups first" or "rings first". Most abstract algebra texts with a "groups first" approach start with some combination of groups in $\mathbb{C}$, groups from modular arithmetic, groups from permutations (including dihedral groups), matrix groups, and then generalize to abstract groups.
Question 1: Why not free groups with relations from the beginning?
Rationale: Working with a free group is almost as general as working with an abstract group, except that you get to explicitly state, for instance, that nothing is commutative, or what the order of an element is, etc. Like $S_n$, all groups can be constructed out of free groups; possibly in a way that's more intuitive than the $S_n$ construction. The popular focus on permutations is great when thinking about groups as acting on something, but it seems that free groups capture the more basic idea that groups are sets that have additional structure and that certain strings of elements are (or are not) equal to other strings of elements. Granted, this is very algebraic/symbolic. But compared to the standard geometric/permutation approach, it seems understanding the awesome generality of free groups would better aid in understanding the properties of a general group.
Question 2: So, does anyone know of an undergraduate abstract algebra text that starts with free groups, relations, presentations, etc?