The goal is essentially the same as MLE. We have an assumed model for $p({\mathbf{x}}_j|{\omega }_j)$ parameterized by $\theta$. We want to classify a feature $\mathbf{x}$ into some class ${\omega }_j$ based on a labeled dataset $\mathcal{D}$. In MLE, we were trying to maximize the likelihood:

In MAP, we instead maximize the a posteriori:

We immediately notice that if $p(\mathbf{\theta })$ is uniform, ${\hat{\mathbf{\theta }}}_{\text{MAP}}={\hat{\mathbf{\theta }}}_{\text{MLE}}$.