Pneumatology refers to the study of the spirit of God also known as the Holy Spirit. It essentially involves taking a systematic class to learn everything about the holy spirit from what it is, its origin, relationships (God, church, believers), its work and much more. A non-Christian would wonder why a person would invest in studying something that we cannot see or touch. It begs the inevitable question of what role pneumatology plays in theology and life in general.
The holy spirit is valuable to Christians. It is the third person of the Trinity (God the Father, God the Son, and God the Holy Spirit) with each being God. Plenty of theological fields focus on exploring the concept of God the Father and Son with minimal academic effort directed at studying the Holy Spirit despite its contribution to Christianity. It is because of this that the idea of holy spirit differs from the other two in mainstream Christianity.
Pneumatology helps give Holy Spirit equal amount of focus given to God the father and God the Son. It helps answer many questions like the origin of the holy spirit, how it works, its main functions, and why Jesus left it in charge among other several concerns tied to the limited knowledge of the holy spirit.
When Jesus ascended to heaven, He said He would not leave humans alone and that He left His ‘friend’ in charge. It only makes sense to unravel what the friend is, why he is in charge, why he was left in charge, and how he operates. The importance of the Holy Spirit in the lives of Christians today is beyond measure and pneumatology helps us get close to estimating its actual value.