It is shown that there is a "universal" group that contains the gauge groups of all Yang-Mills theories as subgroups. An analogue of Yang-Mills theory ("universal gauge theory") with this group as the invariance group is shown to exist in 3+1 space-time dimensions. It has all the topological features of Yang-Mills theory, such as instantons and $\ensuremath{\theta}$ vacua, and is a renormalizable theory at the quantum level. The multi-instanton solutions of this theory are found explicitly. The constraint and the eigenvalue problem for the Hamiltonian are solved exactly for all values of $\ensuremath{\theta}$. It is shown that at the quantum level universal gauge theory has the same spectrum as a (1+1)-dimensional free fermion system.