There are already many systems and libraries that fully cover this topic on the JVM. On the one hand, there are the approaches that deal exclusively with the functional aspects - I don't mean developing new languages here - and on the other hand, the purely reactive approaches. Most of the time, these approaches and frameworks are already well designed, rugged and extensive. They are providing whole new type-systems or new core data-structures. Mostly the usage of these solutions will push you to more significant changes in your existing project.
But you can start programming functional and reactive with the plain JDK.
In the beginning, we will deal with the functional aspects and then combine them with the basic reactive ones. The aim is to shed light on the basic ideas and build minimalist solutions based on the core JDK.