Which of the following theories is primarily concerned with abstract structures and their properties?

The correct answer is focused on Number Theory, a branch of mathematics that is mainly concerned with the properties and relationships of numbers, particularly integers. It explores abstract structures like groups, rings, and fields, which help mathematicians understand the nature and distribution of prime numbers as well as their interactions.

Number Theory emphasizes theoretical aspects and often involves proving theorems about number properties without necessarily applying these concepts to real-world problems. This aligns well with the aspect of "abstract structures," as it delves deeply into the qualities and behavior of numbers in a highly abstract manner.

The other fields listed, while important in their own right, do not primarily focus on abstract structures in the same way. Calculus is concerned with change and motion through derivatives and integrals, Statistics focuses on data collection, analysis, interpretation, and presentation, and Geometry is more related to spatial properties and relationships rather than purely abstract structures.