The branch of science concerned with classifying diseases is nosology.

Here's a breakdown:

* Nosology is the branch of medicine that deals with the classification and naming of diseases.

* It involves creating a system for categorizing illnesses based on their causes, symptoms, and other characteristics.

* The goal of nosology is to facilitate communication among healthcare professionals, track disease trends, and develop effective treatment strategies.

Let me know if you'd like to know more about nosology or other aspects of medical science!