An illustration of formal moduli problems with differential graded Lie algebras

This article provides an exposition to the topic of formal moduli problems, emphasizing its connections with differential graded Lie algebras, and mainly following from Jacob Lurie's DAG X: Formal Moduli Problems. As such, this paper should not be viewed as a presentation of original work, but rather a concise introduction to the subject in the form of a set of organized notes. I hoped to make this paper feel welcoming and insightful for the non-expert enjoyer of derived algebraic geometry, like myself. Enjoy!