A ring [R, +, *] is called a field if it’s non zero elements form an abelian group with respect to the composition ‘*’ i.e. if R is a field, then a belonging to R, where a not equal to zero, implies a${-1}$ belongs to R. With additional structure, more theorems could be proved, but the generality is reduced. So for a two-semester introduction to abstract algebra, something like Gallian, or baby Hungerford is, imo, a much better choice. I think you need to be more specific about the aspect of modern algebra (abstract algebra?) in which you are interested.

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