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I am studying the topology of 4-dimensional manifolds using the mapping class groups of surfaces. Dealing directly with 4-dimensional spaces is challenging, but certain favorable classes such as symplectic 4-manifolds are known to be understood as a "family of surfaces." Furthermore, such families can be concisely expressed in terms of the mapping class groups of surfaces. In this way, I am studying abstract 4-manifolds through the more familiar surfaces where our intuitions work much better. With this approach we can construct various 4-manifolds using elementary arguments and my primary focus lies in addressing questions about the existence of 4-manifolds that satisfy certain restrictions on topological invariants, or other invariants.